Tcl Library Source Code

<td class="#doctools_idxleft" width="35%"><a name="matching"> matching </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/grammar_me/me_intro.html"> grammar::me_intro </a> &#183; <a href="tcllib/files/modules/grammar_peg/peg_interp.html"> grammar::peg::interp </a> &#183; <a href="tcllib/files/apps/pt.html"> pt </a> &#183; <a href="tcllib/files/modules/pt/pt_astree.html"> pt::ast </a> &#183; <a href="tcllib/files/modules/pt/pt_cparam_config_critcl.html"> pt::cparam::configuration::critcl </a> &#183; <a href="tcllib/files/modules/pt/pt_cparam_config_tea.html"> pt::cparam::configuration::tea </a> &#183; <a href="tcllib/files/modules/pt/pt_json_language.html"> pt::json_language </a> &#183; <a href="tcllib/files/modules/pt/pt_param.html"> pt::param </a> &#183; <a href="tcllib/files/modules/pt/pt_pexpression.html"> pt::pe </a> &#183; <a href="tcllib/files/modules/pt/pt_pexpr_op.html"> pt::pe::op </a> &#183; <a href="tcllib/files/modules/pt/pt_pegrammar.html"> pt::peg </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_container.html"> pt::peg::container </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_container_peg.html"> pt::peg::container::peg </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_export.html"> pt::peg::export </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_export_container.html"> pt::peg::export::container </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_export_json.html"> pt::peg::export::json </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_export_peg.html"> pt::peg::export::peg </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_from_container.html"> pt::peg::from::container </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_from_json.html"> pt::peg::from::json </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_from_peg.html"> pt::peg::from::peg </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_import.html"> pt::peg::import </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_import_container.html"> pt::peg::import::container </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_import_json.html"> pt::peg::import::json </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_import_peg.html"> pt::peg::import::peg </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_interp.html"> pt::peg::interp </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_to_container.html"> pt::peg::to::container </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_to_cparam.html"> pt::peg::to::cparam </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_to_json.html"> pt::peg::to::json </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_to_param.html"> pt::peg::to::param </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_to_peg.html"> pt::peg::to::peg </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_to_tclparam.html"> pt::peg::to::tclparam </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_language.html"> pt::peg_language </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_introduction.html"> pt::pegrammar </a> &#183; <a href="tcllib/files/modules/pt/pt_pgen.html"> pt::pgen </a> &#183; <a href="tcllib/files/modules/pt/pt_rdengine.html"> pt::rde </a> &#183; <a href="tcllib/files/modules/pt/pt_tclparam_config_nx.html"> pt::tclparam::configuration::nx </a> &#183; <a href="tcllib/files/modules/pt/pt_tclparam_config_snit.html"> pt::tclparam::configuration::snit </a> &#183; <a href="tcllib/files/modules/pt/pt_tclparam_config_tcloo.html"> pt::tclparam::configuration::tcloo </a> &#183; <a href="tcllib/files/modules/pt/pt_util.html"> pt::util </a> &#183; <a href="tcllib/files/modules/pt/pt_to_api.html"> pt_export_api </a> &#183; <a href="tcllib/files/modules/pt/pt_from_api.html"> pt_import_api </a> &#183; <a href="tcllib/files/modules/pt/pt_introduction.html"> pt_introduction </a> &#183; <a href="tcllib/files/modules/pt/pt_parse_peg.html"> pt_parse_peg </a> &#183; <a href="tcllib/files/modules/pt/pt_parser_api.html"> pt_parser_api </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_op.html"> pt_peg_op </a> &#183; <a href="tcllib/files/modules/struct/graphops.html"> struct::graph::op </a>
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<td class="#doctools_idxleft" width="35%"><a name="math"> math </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/math/math.html"> math </a> &#183; <a href="tcllib/files/modules/math/bigfloat.html"> math::bigfloat </a> &#183; <a href="tcllib/files/modules/math/bignum.html"> math::bignum </a> &#183; <a href="tcllib/files/modules/math/calculus.html"> math::calculus </a> &#183; <a href="tcllib/files/modules/math/qcomplex.html"> math::complexnumbers </a> &#183; <a href="tcllib/files/modules/math/constants.html"> math::constants </a> &#183; <a href="tcllib/files/modules/math/decimal.html"> math::decimal </a> &#183; <a href="tcllib/files/modules/math/fuzzy.html"> math::fuzzy </a> &#183; <a href="tcllib/files/modules/math/math_geometry.html"> math::geometry </a> &#183; <a href="tcllib/files/modules/math/interpolate.html"> math::interpolate </a> &#183; <a href="tcllib/files/modules/math/linalg.html"> math::linearalgebra </a> &#183; <a href="tcllib/files/modules/math/optimize.html"> math::optimize </a> &#183; <a href="tcllib/files/modules/math/pca.html"> math::PCA </a> &#183; <a href="tcllib/files/modules/math/polynomials.html"> math::polynomials </a> &#183; <a href="tcllib/files/modules/math/rational_funcs.html"> math::rationalfunctions </a> &#183; <a href="tcllib/files/modules/math/special.html"> math::special </a> &#183; <a href="tcllib/files/modules/math/trig.html"> math::trig </a> &#183; <a href="tcllib/files/modules/simulation/annealing.html"> simulation::annealing </a> &#183; <a href="tcllib/files/modules/simulation/montecarlo.html"> simulation::montecarlo </a> &#183; <a href="tcllib/files/modules/simulation/simulation_random.html"> simulation::random </a>
</td></tr>
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<td class="#doctools_idxleft" width="35%"><a name="mathematics"> mathematics </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/math/fourier.html"> math::fourier </a> &#183; <a href="tcllib/files/modules/math/statistics.html"> math::statistics </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>

</td></tr>
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<td class="#doctools_idxleft" width="35%"><a name="treeql"> TreeQL </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/treeql/treeql.html"> treeql </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="trigonometry"> trigonometry </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/math/trig.html"> math::trig </a>
</td></tr>
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<td class="#doctools_idxleft" width="35%"><a name="trimming"> trimming </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/textutil/textutil.html"> textutil </a> &#183; <a href="tcllib/files/modules/textutil/trim.html"> textutil::trim </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="twitter"> twitter </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/oauth/oauth.html"> oauth </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="type"> type </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/fileutil/fileutil.html"> fileutil </a> &#183; <a href="tcllib/files/modules/fumagic/cfront.html"> fileutil::magic::cfront </a> &#183; <a href="tcllib/files/modules/fumagic/cgen.html"> fileutil::magic::cgen </a> &#183; <a href="tcllib/files/modules/fumagic/filetypes.html"> fileutil::magic::filetype </a> &#183; <a href="tcllib/files/modules/fumagic/rtcore.html"> fileutil::magic::rt </a> &#183; <a href="tcllib/files/modules/snit/snit.html"> snit </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="type_checking"> Type checking </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/valtype/valtype_common.html"> valtype::common </a> &#183; <a href="tcllib/files/modules/valtype/cc_amex.html"> valtype::creditcard::amex </a> &#183; <a href="tcllib/files/modules/valtype/cc_discover.html"> valtype::creditcard::discover </a> &#183; <a href="tcllib/files/modules/valtype/cc_mastercard.html"> valtype::creditcard::mastercard </a> &#183; <a href="tcllib/files/modules/valtype/cc_visa.html"> valtype::creditcard::visa </a> &#183; <a href="tcllib/files/modules/valtype/ean13.html"> valtype::gs1::ean13 </a> &#183; <a href="tcllib/files/modules/valtype/iban.html"> valtype::iban </a> &#183; <a href="tcllib/files/modules/valtype/imei.html"> valtype::imei </a> &#183; <a href="tcllib/files/modules/valtype/isbn.html"> valtype::isbn </a> &#183; <a href="tcllib/files/modules/valtype/luhn.html"> valtype::luhn </a> &#183; <a href="tcllib/files/modules/valtype/luhn5.html"> valtype::luhn5 </a> &#183; <a href="tcllib/files/modules/valtype/usnpi.html"> valtype::usnpi </a> &#183; <a href="tcllib/files/modules/valtype/verhoeff.html"> valtype::verhoeff </a>
</td></tr>
<tr class="#doctools_idxheader"><th colspan="2">
<a name="cU">Keywords: U</a>
</th></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="uevent"> uevent </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/hook/hook.html"> hook </a>
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<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="unbind"> unbind </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/uev/uevent.html"> uevent </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="uncapitalize"> uncapitalize </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/textutil/textutil_string.html"> textutil::string </a>
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<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="undenting"> undenting </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/textutil/adjust.html"> textutil::adjust </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="unicode"> unicode </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/stringprep/stringprep.html"> stringprep </a> &#183; <a href="tcllib/files/modules/stringprep/stringprep_data.html"> stringprep::data </a> &#183; <a href="tcllib/files/modules/stringprep/unicode.html"> unicode </a> &#183; <a href="tcllib/files/modules/stringprep/unicode_data.html"> unicode::data </a>
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<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="union"> union </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/struct/disjointset.html"> struct::disjointset </a> &#183; <a href="tcllib/files/modules/struct/struct_set.html"> struct::set </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="unit"> unit </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/units/units.html"> units </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="unknown_hooking"> unknown hooking </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/namespacex/namespacex.html"> namespacex </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="untie"> untie </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/tie/tie_std.html"> tie </a> &#183; <a href="tcllib/files/modules/tie/tie.html"> tie </a>
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<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="update"> update </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/coroutine/tcllib_coroutine.html"> coroutine </a> &#183; <a href="tcllib/files/modules/coroutine/coro_auto.html"> coroutine::auto </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="uri"> uri </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/uri/uri.html"> uri </a> &#183; <a href="tcllib/files/modules/uri/urn-scheme.html"> uri_urn </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="url"> url </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/doctools2idx/idx_container.html"> doctools::idx </a> &#183; <a href="tcllib/files/modules/doctools2idx/idx_export.html"> doctools::idx::export </a> &#183; <a href="tcllib/files/modules/doctools2idx/idx_import.html"> doctools::idx::import </a> &#183; <a href="tcllib/files/modules/doctools2toc/toc_export.html"> doctools::toc::export </a> &#183; <a href="tcllib/files/modules/doctools2toc/toc_import.html"> doctools::toc::import </a> &#183; <a href="tcllib/files/modules/map/map_geocode_nominatim.html"> map::geocode::nominatim </a> &#183; <a href="tcllib/files/modules/map/map_slippy_fetcher.html"> map::slippy::fetcher </a> &#183; <a href="tcllib/files/modules/uri/uri.html"> uri </a> &#183; <a href="tcllib/files/modules/uri/urn-scheme.html"> uri_urn </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="urn"> urn </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/uri/urn-scheme.html"> uri_urn </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="us_npi"> US-NPI </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/valtype/usnpi.html"> valtype::usnpi </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="utilities"> utilities </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/namespacex/namespacex.html"> namespacex </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="uuencode"> uuencode </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/base64/uuencode.html"> uuencode </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="uuid"> UUID </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/uuid/uuid.html"> uuid </a>
</td></tr>
<tr class="#doctools_idxheader"><th colspan="2">
<a name="cV">Keywords: V</a>
</th></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="validation"> Validation </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/valtype/valtype_common.html"> valtype::common </a> &#183; <a href="tcllib/files/modules/valtype/cc_amex.html"> valtype::creditcard::amex </a> &#183; <a href="tcllib/files/modules/valtype/cc_discover.html"> valtype::creditcard::discover </a> &#183; <a href="tcllib/files/modules/valtype/cc_mastercard.html"> valtype::creditcard::mastercard </a> &#183; <a href="tcllib/files/modules/valtype/cc_visa.html"> valtype::creditcard::visa </a> &#183; <a href="tcllib/files/modules/valtype/ean13.html"> valtype::gs1::ean13 </a> &#183; <a href="tcllib/files/modules/valtype/iban.html"> valtype::iban </a> &#183; <a href="tcllib/files/modules/valtype/imei.html"> valtype::imei </a> &#183; <a href="tcllib/files/modules/valtype/isbn.html"> valtype::isbn </a> &#183; <a href="tcllib/files/modules/valtype/luhn.html"> valtype::luhn </a> &#183; <a href="tcllib/files/modules/valtype/luhn5.html"> valtype::luhn5 </a> &#183; <a href="tcllib/files/modules/valtype/usnpi.html"> valtype::usnpi </a> &#183; <a href="tcllib/files/modules/valtype/verhoeff.html"> valtype::verhoeff </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="value_checking"> Value checking </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/valtype/valtype_common.html"> valtype::common </a> &#183; <a href="tcllib/files/modules/valtype/cc_amex.html"> valtype::creditcard::amex </a> &#183; <a href="tcllib/files/modules/valtype/cc_discover.html"> valtype::creditcard::discover </a> &#183; <a href="tcllib/files/modules/valtype/cc_mastercard.html"> valtype::creditcard::mastercard </a> &#183; <a href="tcllib/files/modules/valtype/cc_visa.html"> valtype::creditcard::visa </a> &#183; <a href="tcllib/files/modules/valtype/ean13.html"> valtype::gs1::ean13 </a> &#183; <a href="tcllib/files/modules/valtype/iban.html"> valtype::iban </a> &#183; <a href="tcllib/files/modules/valtype/imei.html"> valtype::imei </a> &#183; <a href="tcllib/files/modules/valtype/isbn.html"> valtype::isbn </a> &#183; <a href="tcllib/files/modules/valtype/luhn.html"> valtype::luhn </a> &#183; <a href="tcllib/files/modules/valtype/luhn5.html"> valtype::luhn5 </a> &#183; <a href="tcllib/files/modules/valtype/usnpi.html"> valtype::usnpi </a> &#183; <a href="tcllib/files/modules/valtype/verhoeff.html"> valtype::verhoeff </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="vectors"> vectors </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/math/linalg.html"> math::linearalgebra </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="verhoeff"> verhoeff </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/valtype/verhoeff.html"> valtype::verhoeff </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="vertex"> vertex </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/struct/graph.html"> struct::graph </a> &#183; <a href="tcllib/files/modules/struct/graphops.html"> struct::graph::op </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="vertex_cover"> vertex cover </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/struct/graphops.html"> struct::graph::op </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="virtual_channel"> virtual channel </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/virtchannel_base/cat.html"> tcl::chan::cat </a> &#183; <a href="tcllib/files/modules/virtchannel_core/core.html"> tcl::chan::core </a> &#183; <a href="tcllib/files/modules/virtchannel_core/events.html"> tcl::chan::events </a> &#183; <a href="tcllib/files/modules/virtchannel_base/facade.html"> tcl::chan::facade </a> &#183; <a href="tcllib/files/modules/virtchannel_base/tcllib_fifo.html"> tcl::chan::fifo </a> &#183; <a href="tcllib/files/modules/virtchannel_base/tcllib_fifo2.html"> tcl::chan::fifo2 </a> &#183; <a href="tcllib/files/modules/virtchannel_base/halfpipe.html"> tcl::chan::halfpipe </a> &#183; <a href="tcllib/files/modules/virtchannel_base/tcllib_memchan.html"> tcl::chan::memchan </a> &#183; <a href="tcllib/files/modules/virtchannel_base/tcllib_null.html"> tcl::chan::null </a> &#183; <a href="tcllib/files/modules/virtchannel_base/nullzero.html"> tcl::chan::nullzero </a> &#183; <a href="tcllib/files/modules/virtchannel_base/tcllib_random.html"> tcl::chan::random </a> &#183; <a href="tcllib/files/modules/virtchannel_base/std.html"> tcl::chan::std </a> &#183; <a href="tcllib/files/modules/virtchannel_base/tcllib_string.html"> tcl::chan::string </a> &#183; <a href="tcllib/files/modules/virtchannel_base/textwindow.html"> tcl::chan::textwindow </a> &#183; <a href="tcllib/files/modules/virtchannel_base/tcllib_variable.html"> tcl::chan::variable </a> &#183; <a href="tcllib/files/modules/virtchannel_base/tcllib_zero.html"> tcl::chan::zero </a> &#183; <a href="tcllib/files/modules/virtchannel_base/randseed.html"> tcl::randomseed </a> &#183; <a href="tcllib/files/modules/virtchannel_transform/adler32.html"> tcl::transform::adler32 </a> &#183; <a href="tcllib/files/modules/virtchannel_transform/vt_base64.html"> tcl::transform::base64 </a> &#183; <a href="tcllib/files/modules/virtchannel_core/transformcore.html"> tcl::transform::core </a> &#183; <a href="tcllib/files/modules/virtchannel_transform/vt_counter.html"> tcl::transform::counter </a> &#183; <a href="tcllib/files/modules/virtchannel_transform/vt_crc32.html"> tcl::transform::crc32 </a> &#183; <a href="tcllib/files/modules/virtchannel_transform/hex.html"> tcl::transform::hex </a> &#183; <a href="tcllib/files/modules/virtchannel_transform/identity.html"> tcl::transform::identity </a> &#183; <a href="tcllib/files/modules/virtchannel_transform/limitsize.html"> tcl::transform::limitsize </a> &#183; <a href="tcllib/files/modules/virtchannel_transform/observe.html"> tcl::transform::observe </a> &#183; <a href="tcllib/files/modules/virtchannel_transform/vt_otp.html"> tcl::transform::otp </a> &#183; <a href="tcllib/files/modules/virtchannel_transform/rot.html"> tcl::transform::rot </a> &#183; <a href="tcllib/files/modules/virtchannel_transform/spacer.html"> tcl::transform::spacer </a> &#183; <a href="tcllib/files/modules/virtchannel_transform/tcllib_zlib.html"> tcl::transform::zlib </a>
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<td class="#doctools_idxleft" width="35%"><a name="visa"> VISA </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/valtype/cc_visa.html"> valtype::creditcard::visa </a>
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<td class="#doctools_idxleft" width="35%"><a name="vwait"> vwait </a></td>
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<a name="cW">Keywords: W</a>
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<td class="#doctools_idxleft" width="35%"><a name="wais"> wais </a></td>
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<a href="tcllib/files/modules/uri/uri.html"> uri </a>
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<td class="#doctools_idxleft" width="35%"><a name="widget"> widget </a></td>
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<td class="#doctools_idxleft" width="35%"><a name="widget_adaptors"> widget adaptors </a></td>
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<td class="#doctools_idxleft" width="35%"><a name="wiki"> wiki </a></td>
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<td class="#doctools_idxleft" width="35%"><a name="word"> word </a></td>
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<a href="tcllib/files/modules/httpd/httpd.html"> tool </a>
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<td class="#doctools_idxleft" width="35%"><a name="www"> www </a></td>
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<tr class="#doctools_idxheader"><th colspan="2">
<a name="cX">Keywords: X</a>
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<td class="#doctools_idxleft" width="35%"><a name="x_208"> x.208 </a></td>
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<a href="tcllib/files/modules/asn/asn.html"> asn </a>
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<td class="#doctools_idxleft" width="35%"><a name="x_209"> x.209 </a></td>
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<a href="tcllib/files/modules/asn/asn.html"> asn </a>
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<td class="#doctools_idxleft" width="35%"><a name="xgoogletoken"> XGoogleToken </a></td>
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<a href="tcllib/files/modules/sasl/gtoken.html"> SASL::XGoogleToken </a>
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<td class="#doctools_idxleft" width="35%"><a name="xml"> xml </a></td>
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<a href="tcllib/files/modules/amazon-s3/xsxp.html"> xsxp </a>
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<a href="tcllib/files/modules/virtchannel_transform/vt_otp.html"> tcl::transform::otp </a>
</td></tr>
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<a href="tcllib/files/modules/treeql/treeql.html"> treeql </a>
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<a href="tcllib/files/modules/treeql/treeql.html"> treeql </a>
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<td class="#doctools_idxleft" width="35%"><a name="yaml"> yaml </a></td>
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<td class="#doctools_idxleft" width="35%"><a name="ydecode"> ydecode </a></td>
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<a href="tcllib/files/modules/base64/yencode.html"> yencode </a>
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<a href="tcllib/files/modules/base64/yencode.html"> yencode </a>
</td></tr>
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<td class="#doctools_idxleft" width="35%"><a name="yencode"> yencode </a></td>
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<a href="tcllib/files/modules/base64/yencode.html"> yencode </a>
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<a href="tcllib/files/modules/virtchannel_base/nullzero.html"> tcl::chan::nullzero </a> &#183; <a href="tcllib/files/modules/virtchannel_base/tcllib_zero.html"> tcl::chan::zero </a>
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<a href="tcllib/files/modules/zip/decode.html"> zipfile::decode </a> &#183; <a href="tcllib/files/modules/zip/encode.html"> zipfile::encode </a> &#183; <a href="tcllib/files/modules/zip/mkzip.html"> zipfile::mkzip </a>
</td></tr>
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<td class="#doctools_idxleft" width="35%"><a name="zlib"> zlib </a></td>
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<a href="tcllib/files/modules/virtchannel_transform/tcllib_zlib.html"> tcl::transform::zlib </a>
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<td class="#doctools_idxleft" width="35%"><a name="zoom"> zoom </a></td>
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<a href="tcllib/files/modules/map/map_slippy.html"> map::slippy </a> &#183; <a href="tcllib/files/modules/map/map_slippy_cache.html"> map::slippy::cache </a> &#183; <a href="tcllib/files/modules/map/map_slippy_fetcher.html"> map::slippy::fetcher </a>
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</table>

<div class='fossil-doc' data-title='cache::async - In-memory caches'>
<style>
    HTML {
	background: 	#FFFFFF;
	color: 		black;
    }
    BODY {

| <a href="../../../toc.html">Table Of Contents</a>
| <a href="../../../../index.html">Keyword Index</a>
| <a href="../../../../toc0.html">Categories</a>
| <a href="../../../../toc1.html">Modules</a>
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 ] <hr>
<div class="doctools">
<h1 class="doctools_title">cache::async(n) 0.3.1 tcllib &quot;In-memory caches&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>cache::async - Asynchronous in-memory cache</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">API</a></li>
<li class="doctools_section"><a href="#section3">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.4</b></li>
<li>package require <b class="pkgname">cache::async <span class="opt">?0.3.1?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::cache::async</b> <i class="arg">objectName</i> <i class="arg">commandprefix</i> <span class="opt">?<i class="arg">options</i>...?</span></a></li>
<li><a href="#2"><i class="arg">objectName</i> <b class="method">get</b> <i class="arg">key</i> <i class="arg">donecmdprefix</i></a></li>
<li><a href="#3"><i class="arg">objectName</i> <b class="method">set</b> <i class="arg">key</i> <i class="arg">value</i></a></li>
<li><a href="#4"><i class="arg">objectName</i> <b class="method">unset</b> <i class="arg">key</i></a></li>
<li><a href="#5"><i class="arg">objectName</i> <b class="method">exists</b> <i class="arg">key</i></a></li>

<li><a href="#5"><b class="cmd">::cron::object_coroutine</b> <i class="arg">object</i> <i class="arg">coroutine</i> <i class="arg">?info?</i></a></li>
<li><a href="#6"><b class="cmd">::cron::sleep</b> <i class="arg">milliseconds</i></a></li>
<li><a href="#7"><b class="cmd">::cron::task delete</b> <i class="arg">process</i></a></li>
<li><a href="#8"><b class="cmd">::cron::task exists</b> <i class="arg">process</i></a></li>
<li><a href="#9"><b class="cmd">::cron::task info</b> <i class="arg">process</i></a></li>
<li><a href="#10"><b class="cmd">::cron::task set</b> <i class="arg">process</i> <i class="arg">field</i> <i class="arg">value</i> <i class="arg">?field...?</i> <i class="arg">?value...?</i></a></li>
<li><a href="#11"><b class="cmd">::cron::wake</b> <i class="arg">?who?</i></a></li>
<li><a href="#12"><b class="cmd">::cron::clock_step</b> <i class="arg">milliseconds</i></a></li>
<li><a href="#13"><b class="cmd">::cron::clock_delay</b> <i class="arg">milliseconds</i></a></li>
<li><a href="#14"><b class="cmd">::cron::clock_sleep</b> <i class="arg">seconds</i> <i class="arg">?offset?</i></a></li>
<li><a href="#15"><b class="cmd">::cron::clock_set</b> <i class="arg">newtime</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>The <b class="package">cron</b> package provides a Pure-tcl set of tools to allow

<dt><a name="8"><b class="cmd">::cron::task exists</b> <i class="arg">process</i></a></dt>
<dd><p>Returns true if <i class="arg">process</i> is registered with cron.</p></dd>
<dt><a name="9"><b class="cmd">::cron::task info</b> <i class="arg">process</i></a></dt>
<dd><p>Returns a dict describing <i class="arg">process</i>. See <b class="cmd">::cron::task set</b> for a description of the options.</p></dd>
<dt><a name="10"><b class="cmd">::cron::task set</b> <i class="arg">process</i> <i class="arg">field</i> <i class="arg">value</i> <i class="arg">?field...?</i> <i class="arg">?value...?</i></a></dt>
<dd><p>If <i class="arg">process</i> does not exist, it is created. Options Include:</p>
<dl class="doctools_definitions">
<dt><b class="cmd"><a href="../../../../index.html#command">command</a></b></dt>
<dd><p>If <b class="cmd"><a href="../coroutine/tcllib_coroutine.html">coroutine</a></b> is black, a global command which implements this process. If <b class="cmd"><a href="../coroutine/tcllib_coroutine.html">coroutine</a></b> is not
black, the command to invoke to create or recreate the coroutine.</p></dd>
<dt><b class="cmd"><a href="../coroutine/tcllib_coroutine.html">coroutine</a></b></dt>
<dd><p>The name of the coroutine (if any) which implements this process.</p></dd>
<dt><b class="cmd">frequency</b></dt>
<dd><p>If -1, this process is terminated after the next event. If 0 this process should be called during every
idle event. If positive, this process should generate events periodically. The frequency is an integer number
of milliseconds between events.</p></dd>
<dt><b class="cmd"><a href="../../../../index.html#object">object</a></b></dt>
<dd><p>The object associated with this process or coroutine.</p></dd>
<dt><b class="cmd">scheduled</b></dt>
<dd><p>If non-zero, the absolute time from the epoch (in milliseconds) that this process will trigger an event.
If zero, and the <b class="cmd">frequency</b> is also zero, this process is called every idle loop.</p></dd>
<dt><b class="cmd"><a href="../../../../index.html#running">running</a></b></dt>
<dd><p>A boolean flag. If true it indicates the process never returned or yielded during the event loop,
and will not be called again until it does so.</p></dd>
</dl></dd>
<dt><a name="11"><b class="cmd">::cron::wake</b> <i class="arg">?who?</i></a></dt>
<dd><p>Wake up cron, and arrange for its event loop to be run during the next Idle cycle.</p>
<pre class="doctools_example">
::cron::wake {I just did something important}
</pre>
</dd>
</dl>
<p>Several utility commands are provided that are used internally within cron and for
testing cron, but may or may not be useful in the general cases.</p>
<dl class="doctools_definitions">
<dt><a name="12"><b class="cmd">::cron::clock_step</b> <i class="arg">milliseconds</i></a></dt>
<dd><p>Return a clock time absolute to the epoch which falls on the next
border between one second and the next for the value of <i class="arg">milliseconds</i></p></dd>
<dt><a name="13"><b class="cmd">::cron::clock_delay</b> <i class="arg">milliseconds</i></a></dt>
<dd><p>Return a clock time absolute to the epoch which falls on the next
border between one second and the next <i class="arg">milliseconds</i> in the future.</p></dd>
<dt><a name="14"><b class="cmd">::cron::clock_sleep</b> <i class="arg">seconds</i> <i class="arg">?offset?</i></a></dt>
<dd><p>Return a clock time absolute to the epoch which falls exactly <i class="arg">seconds</i> in
the future. If offset is given it may be positive or negative, and will shift
the final time to before or after the second would flip.</p></dd>
<dt><a name="15"><b class="cmd">::cron::clock_set</b> <i class="arg">newtime</i></a></dt>
<dd><p>Sets the internal clock for cron. This command will advance the time in 100ms
increment, triggering events, until the internal time catches up with <i class="arg">newtime</i>.</p>
<p><i class="arg">newtime</i> is expressed in absolute milliseconds since the beginning of the epoch.</p></dd>
</dl>
</div>
<div id="section3" class="doctools_section"><h2><a name="section3">Bugs, Ideas, Feedback</a></h2>
<p>This document, and the package it describes, will undoubtedly contain
bugs and other problems.
Please report such in the category <em>odie</em> of the
<a href="http://core.tcl.tk/tcllib/reportlist">Tcllib Trackers</a>.

<dt>varname <i class="arg">fvar</i> (in)</dt>
<dd><p>Has to refer to an array variable. Keys are strings containing
date, author of a log entry, and a comment for that entry, in this
order, separated by commas.</p>
<p>The values are lists of the files the entry is touching.</p></dd>
</dl></dd>
<dt><a name="2"><b class="cmd">::doctools::cvs::toChangeLog</b> <i class="arg">evar</i> <i class="arg">cvar</i> <i class="arg">fvar</i></a></dt>

<dd><p>The three arguments for this command are the same as the last three
arguments of the command <b class="cmd">::doctools::cvs::scanLog</b>. This command
however expects them to be filled with information about one or more
logs. It takes this information and converts it into a text in the
format of a ChangeLog as accepted and generated by <b class="syscmd"><a href="../../../../index.html#emacs">emacs</a></b>. The
constructed text is returned as the result of the command.</p></dd>
</dl>
</div>

[<b class="cmd">require   PACKAGE</b>]
[description]
[manpage_end]
</pre>
<p>Remember that the whitespace is optional. The document</p>
<pre class="doctools_example">
    [manpage_begin NAME SECTION VERSION]










    [copyright {YEAR AUTHOR}][titledesc TITLE][moddesc MODULE_TITLE]
    [require PACKAGE VERSION][require PACKAGE][description]
    [vset CATEGORY doctools]
[include ../doctools2base/include/feedback.inc]
[manpage_end]
</pre>
<p>has the same meaning as the example before.</p>

<p>The example demonstrating the use of text markup is an excerpt from
the <i class="term"><a href="doctools_lang_cmdref.html">doctools language command reference</a></i>, with some
highlighting added.
It shows their use within a block of text, as the arguments of a list
item command (<b class="cmd">call</b>), and our ability to nest them.</p>
<pre class="doctools_example">
  ...
  [call [<b class="cmd">cmd arg_def</b>] [<b class="cmd">arg type</b>] [<b class="cmd">arg name</b>] [<b class="cmd">opt</b> [<b class="cmd">arg mode</b>]]]
  Text structure. List element. Argument list. Automatically closes the
  previous list element. Specifies the data-[<b class="cmd">arg type</b>] of the described
  argument of a command, its [<b class="cmd">arg name</b>] and its i/o-[<b class="cmd">arg mode</b>]. The
  latter is optional.
  ...
</pre>
</div>

<div class='fossil-doc' data-title='lazyset - Lazy evaluation for variables and arrays'>
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 <hr> [
   <a href="../../../../toc.html">Main Table Of Contents</a>
| <a href="../../../toc.html">Table Of Contents</a>
| <a href="../../../../index.html">Keyword Index</a>
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 ] <hr>
<div class="doctools">
<h1 class="doctools_title">lazyset(n) 1 tcllib &quot;Lazy evaluation for variables and arrays&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>lazyset - Lazy evaluation</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">COMMANDS</a></li>
<li class="doctools_section"><a href="#section3">EXAMPLES</a></li>
<li class="doctools_section"><a href="#section4">AUTHORS</a></li>
<li class="doctools_section"><a href="#section5">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.5</b></li>
<li>package require <b class="pkgname">lazyset <span class="opt">?1?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::lazyset::variable</b> <span class="opt">?<i class="arg">-array boolean</i>?</span> <span class="opt">?<i class="arg">-appendArgs boolean</i>?</span> <i class="arg">variableName</i> <i class="arg">commandPrefix</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>The <b class="package">lazyset</b> package provides a mechanism for deferring execution
of code until a specific variable or any index of an array is referenced.</p>
</div>
<div id="section2" class="doctools_section"><h2><a name="section2">COMMANDS</a></h2>
<dl class="doctools_definitions">
<dt><a name="1"><b class="cmd">::lazyset::variable</b> <span class="opt">?<i class="arg">-array boolean</i>?</span> <span class="opt">?<i class="arg">-appendArgs boolean</i>?</span> <i class="arg">variableName</i> <i class="arg">commandPrefix</i></a></dt>
<dd><p>Arrange for the code specified as <i class="arg">commandPrefix</i> to be executed when
the variable whose name is specified by <i class="arg">variableName</i> is read for
the first time.
If the optional argument <i class="arg">-array boolean</i> is specified as true,
then the variable specified as <i class="arg">variableName</i> is treated as an
array and attempting to read any index of the array causes that
index to be set by the <i class="arg">commandPrefix</i> as they are read.
If the optional argument <i class="arg">-appendArgs boolean</i> is specified as
false, then the variable name and subnames are not appended to the
<i class="arg">commandPrefix</i> before it is evaluated.  If the argument
<i class="arg">-appendArgs boolean</i> is not specified or is specified as true
then 1 or 2 additional arguments are appended to the <i class="arg">commandPrefix</i>.
If <i class="arg">-array boolean</i> is specified as true, then 2 arguments are
appended corresponding to the name of the variable and the index,
otherwise 1 argument is appended containing the name of variable.
The <i class="arg">commandPrefix</i> code is run in the same scope as the variable
is read.</p></dd>
</dl>
</div>
<div id="section3" class="doctools_section"><h2><a name="section3">EXAMPLES</a></h2>
<pre class="doctools_example">
	::lazyset::variable page {apply {{name} {
		package require http
		set token [http::geturl http://www.tcl.tk/]
		set data [http::data $token]
		return $data
	}}}
	puts $page
</pre>
<pre class="doctools_example">
	::lazyset::variable -array true page {apply {{name index} {
		package require http
		set token [http::geturl $index]
		set data [http::data $token]
		return $data
	}}}
	puts $page(http://www.tcl.tk/)
</pre>
<pre class="doctools_example">
	::lazyset::variable -appendArgs false simple {
		return -level 0 42
	}
	puts $simple
</pre>
</div>
<div id="section4" class="doctools_section"><h2><a name="section4">AUTHORS</a></h2>
<p>Roy Keene</p>
</div>
<div id="section5" class="doctools_section"><h2><a name="section5">Bugs, Ideas, Feedback</a></h2>
<p>This document, and the package it describes, will undoubtedly contain
bugs and other problems.
Please report such in the category <em>utility</em> of the
<a href="http://core.tcl.tk/tcllib/reportlist">Tcllib Trackers</a>.
Please also report any ideas for enhancements you may have for either
package and/or documentation.</p>
<p>When proposing code changes, please provide <em>unified diffs</em>,
i.e the output of <b class="const">diff -u</b>.</p>
<p>Note further that <em>attachments</em> are strongly preferred over
inlined patches. Attachments can be made by going to the <b class="const">Edit</b>
form of the ticket immediately after its creation, and then using the
left-most button in the secondary navigation bar.</p>
</div>
<div id="category" class="doctools_section"><h2><a name="category">Category</a></h2>
<p>Utility</p>
</div>
<div id="copyright" class="doctools_section"><h2><a name="copyright">Copyright</a></h2>
<p>Copyright &copy; 2018 Roy Keene</p>
</div>
</div>

<dd><p>Compares two levels (including unique abbreviations) with respect to
their priority. This command can be used by the -command option of
lsort. The result is one of -1, 0 or 1 or an error. A result of -1
signals that level1 is of less priority than level2. 0 signals that
both levels have the same priority. 1 signals that level1 has higher
priority than level2.</p></dd>
<dt><a name="8"><b class="cmd">::log::lvSuppress</b> <i class="arg">level</i> {<i class="arg">suppress</i> 1}</a></dt>

<dd><p>(Un)suppresses the output of messages having the specified
level. Unique abbreviations for the level are allowed here too.</p></dd>
<dt><a name="9"><b class="cmd">::log::lvSuppressLE</b> <i class="arg">level</i> {<i class="arg">suppress</i> 1}</a></dt>

<dd><p>(Un)suppresses the output of messages having the specified level or
one of lesser priority. Unique abbreviations for the level are allowed
here too.</p></dd>
<dt><a name="10"><b class="cmd">::log::lvIsSuppressed</b> <i class="arg">level</i></a></dt>
<dd><p>Asks the package whether the specified level is currently
suppressed. Unique abbreviations of level names are allowed.</p></dd>
<dt><a name="11"><b class="cmd">::log::lvCmd</b> <i class="arg">level</i> <i class="arg">cmd</i></a></dt>
<dd><p>Defines for the specified level with which command to write the

<li><p><em>polyline</em> - a list of an even number of coordinates,
interpreted as the x- and y-coordinates of an ordered set of points.</p></li>
<li><p><em>polygon</em> - like a polyline, but the implicit assumption is that
the polyline is closed (if the first and last points do not coincide,
the missing segment is automatically added).</p></li>
<li><p><em>point set</em> - again a list of an even number of coordinates, but
the points are regarded without any ordering.</p></li>
<li><p><em>circle</em> - a list of three numbers, the first two are the coordinates of the
centre and the third is the radius.</p></li>
</ul>
</div>
<div id="section2" class="doctools_section"><h2><a name="section2">PROCEDURES</a></h2>
<p>The package defines the following public procedures:</p>
<dl class="doctools_definitions">
<dt><a name="1"><b class="cmd">::math::geometry::+</b> <i class="arg">point1</i> <i class="arg">point2</i></a></dt>

<dd><p>Line to be checked</p></dd>
<dt>list <i class="arg">circle</i></dt>
<dd><p>Circle that may or may not be intersected</p></dd>
</dl></dd>
<dt><a name="47"><b class="cmd">::math::geometry::intersectionCircleWithCircle</b> <i class="arg">circle1</i> <i class="arg">circle2</i></a></dt>
<dd><p>Determine the points at which the given two circles intersect. There can
be zero, one or two points. (If the two circles touch the circle or are very close,
then one point is returned. An arbitrary margin of 1.0e-10 times the mean of the radii of
the two circles is used to determine this situation.)</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">circle1</i></dt>
<dd><p>First circle</p></dd>
<dt>list <i class="arg">circle2</i></dt>
<dd><p>Second circle</p></dd>
</dl></dd>
<dt><a name="48"><b class="cmd">::math::geometry::tangentLinesToCircle</b> <i class="arg">point</i> <i class="arg">circle</i></a></dt>

<div class='fossil-doc' data-title='math::numtheory - Tcl Math Library'>
<style>
    HTML {
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	color: 		black;
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    BODY {

| <a href="../../../toc.html">Table Of Contents</a>
| <a href="../../../../index.html">Keyword Index</a>
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 ] <hr>
<div class="doctools">
<h1 class="doctools_title">math::numtheory(n) 1.1.1 tcllib &quot;Tcl Math Library&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>math::numtheory - Number Theory</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl <span class="opt">?8.5?</span></b></li>
<li>package require <b class="pkgname">math::numtheory <span class="opt">?1.1.1?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">math::numtheory::isprime</b> <i class="arg">N</i> <span class="opt">?<i class="arg">option</i> <i class="arg">value</i> ...?</span></a></li>
<li><a href="#2"><b class="cmd">math::numtheory::firstNprimes</b> <i class="arg">N</i></a></li>
<li><a href="#3"><b class="cmd">math::numtheory::primesLowerThan</b> <i class="arg">N</i></a></li>
<li><a href="#4"><b class="cmd">math::numtheory::primeFactors</b> <i class="arg">N</i></a></li>
<li><a href="#5"><b class="cmd">math::numtheory::primesLowerThan</b> <i class="arg">N</i></a></li>
<li><a href="#6"><b class="cmd">math::numtheory::primeFactors</b> <i class="arg">N</i></a></li>
<li><a href="#7"><b class="cmd">math::numtheory::uniquePrimeFactors</b> <i class="arg">N</i></a></li>
<li><a href="#8"><b class="cmd">math::numtheory::factors</b> <i class="arg">N</i></a></li>
<li><a href="#9"><b class="cmd">math::numtheory::totient</b> <i class="arg">N</i></a></li>
<li><a href="#10"><b class="cmd">math::numtheory::moebius</b> <i class="arg">N</i></a></li>
<li><a href="#11"><b class="cmd">math::numtheory::legendre</b> <i class="arg">a</i> <i class="arg">p</i></a></li>
<li><a href="#12"><b class="cmd">math::numtheory::jacobi</b> <i class="arg">a</i> <i class="arg">b</i></a></li>
<li><a href="#13"><b class="cmd">math::numtheory::gcd</b> <i class="arg">m</i> <i class="arg">n</i></a></li>
<li><a href="#14"><b class="cmd">math::numtheory::lcm</b> <i class="arg">m</i> <i class="arg">n</i></a></li>
<li><a href="#15"><b class="cmd">math::numtheory::numberPrimesGauss</b> <i class="arg">N</i></a></li>
<li><a href="#16"><b class="cmd">math::numtheory::numberPrimesLegendre</b> <i class="arg">N</i></a></li>
<li><a href="#17"><b class="cmd">math::numtheory::numberPrimesLegendreModified</b> <i class="arg">N</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>This package is for collecting various number-theoretic operations, with
a slight bias to prime numbers.</p>
<dl class="doctools_definitions">

</dl></dd>
<dt><a name="4"><b class="cmd">math::numtheory::primeFactors</b> <i class="arg">N</i></a></dt>
<dd><p>Return a list of the prime numbers in the number N</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number to be factorised</p></dd>
</dl></dd>
<dt><a name="5"><b class="cmd">math::numtheory::primesLowerThan</b> <i class="arg">N</i></a></dt>
<dd><p>Return the prime numbers lower/equal to N</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Maximum number to consider</p></dd>
</dl></dd>
<dt><a name="6"><b class="cmd">math::numtheory::primeFactors</b> <i class="arg">N</i></a></dt>
<dd><p>Return a list of the prime numbers in the number N</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number to be factorised</p></dd>
</dl></dd>
<dt><a name="7"><b class="cmd">math::numtheory::uniquePrimeFactors</b> <i class="arg">N</i></a></dt>
<dd><p>Return a list of the <em>unique</em> prime numbers in the number N</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number to be factorised</p></dd>
</dl></dd>
<dt><a name="8"><b class="cmd">math::numtheory::factors</b> <i class="arg">N</i></a></dt>
<dd><p>Return a list of all <em>unique</em> factors in the number N, including 1 and N itself</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number to be factorised</p></dd>
</dl></dd>
<dt><a name="9"><b class="cmd">math::numtheory::totient</b> <i class="arg">N</i></a></dt>
<dd><p>Evaluate the Euler totient function for the number N (number of numbers
relatively prime to N)</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number in question</p></dd>
</dl></dd>
<dt><a name="10"><b class="cmd">math::numtheory::moebius</b> <i class="arg">N</i></a></dt>
<dd><p>Evaluate the Moebius function for the number N</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number in question</p></dd>
</dl></dd>
<dt><a name="11"><b class="cmd">math::numtheory::legendre</b> <i class="arg">a</i> <i class="arg">p</i></a></dt>
<dd><p>Evaluate the Legendre symbol (a/p)</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">a</i> (in)</dt>
<dd><p>Upper number in the symbol</p></dd>
<dt>integer <i class="arg">p</i> (in)</dt>
<dd><p>Lower number in the symbol (must be non-zero)</p></dd>
</dl></dd>
<dt><a name="12"><b class="cmd">math::numtheory::jacobi</b> <i class="arg">a</i> <i class="arg">b</i></a></dt>
<dd><p>Evaluate the Jacobi symbol (a/b)</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">a</i> (in)</dt>
<dd><p>Upper number in the symbol</p></dd>
<dt>integer <i class="arg">b</i> (in)</dt>
<dd><p>Lower number in the symbol (must be odd)</p></dd>
</dl></dd>
<dt><a name="13"><b class="cmd">math::numtheory::gcd</b> <i class="arg">m</i> <i class="arg">n</i></a></dt>
<dd><p>Return the greatest common divisor of <i class="term">m</i> and <i class="term">n</i></p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">m</i> (in)</dt>
<dd><p>First number</p></dd>
<dt>integer <i class="arg">n</i> (in)</dt>
<dd><p>Second number</p></dd>
</dl></dd>
<dt><a name="14"><b class="cmd">math::numtheory::lcm</b> <i class="arg">m</i> <i class="arg">n</i></a></dt>
<dd><p>Return the lowest common multiple of <i class="term">m</i> and <i class="term">n</i></p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">m</i> (in)</dt>
<dd><p>First number</p></dd>
<dt>integer <i class="arg">n</i> (in)</dt>
<dd><p>Second number</p></dd>
</dl></dd>
<dt><a name="15"><b class="cmd">math::numtheory::numberPrimesGauss</b> <i class="arg">N</i></a></dt>
<dd><p>Estimate the number of primes according the formula by Gauss.</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number in question</p></dd>
</dl></dd>
<dt><a name="16"><b class="cmd">math::numtheory::numberPrimesLegendre</b> <i class="arg">N</i></a></dt>
<dd><p>Estimate the number of primes according the formula by Legendre.</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number in question</p></dd>
</dl></dd>
<dt><a name="17"><b class="cmd">math::numtheory::numberPrimesLegendreModified</b> <i class="arg">N</i></a></dt>
<dd><p>Estimate the number of primes according the modified formula by Legendre.</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number in question</p></dd>
</dl></dd>
</dl>
</div>

<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.5</b></li>
<li>package require <b class="pkgname">math::statistics 1</b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::math::statistics::mean</b> <i class="arg">data</i></a></li>
<li><a href="#2"><b class="cmd">::math::statistics::min</b> <i class="arg">data</i></a></li>
<li><a href="#3"><b class="cmd">::math::statistics::max</b> <i class="arg">data</i></a></li>
<li><a href="#4"><b class="cmd">::math::statistics::number</b> <i class="arg">data</i></a></li>

<li><a href="#37"><b class="cmd">::math::statistics::analyse-Kruskal-Wallis</b> <i class="arg">args</i></a></li>
<li><a href="#38"><b class="cmd">::math::statistics::group-rank</b> <i class="arg">args</i></a></li>
<li><a href="#39"><b class="cmd">::math::statistics::test-Wilcoxon</b> <i class="arg">sample_a</i> <i class="arg">sample_b</i></a></li>
<li><a href="#40"><b class="cmd">::math::statistics::spearman-rank</b> <i class="arg">sample_a</i> <i class="arg">sample_b</i></a></li>
<li><a href="#41"><b class="cmd">::math::statistics::spearman-rank-extended</b> <i class="arg">sample_a</i> <i class="arg">sample_b</i></a></li>
<li><a href="#42"><b class="cmd">::math::statistics::kernel-density</b> <i class="arg">data</i> opt <i class="arg">-option value</i> ...</a></li>
<li><a href="#43"><b class="cmd">::math::statistics::bootstrap</b> <i class="arg">data</i> <i class="arg">sampleSize</i> <span class="opt">?numberSamples?</span></a></li>
<li><a href="#44"><b class="cmd">::math::statistics::wasserstein-distance</b> <i class="arg">prob1</i> <i class="arg">prob2</i></a></li>
<li><a href="#45"><b class="cmd">::math::statistics::kl-divergence</b> <i class="arg">prob1</i> <i class="arg">prob2</i></a></li>
<li><a href="#46"><b class="cmd">::math::statistics::logistic-model</b> <i class="arg">xdata</i> <i class="arg">ydata</i></a></li>
<li><a href="#47"><b class="cmd">::math::statistics::logistic-probability</b> <i class="arg">coeffs</i> <i class="arg">x</i></a></li>
<li><a href="#48"><b class="cmd">::math::statistics::tstat</b> <i class="arg">dof</i> <span class="opt">?alpha?</span></a></li>
<li><a href="#49"><b class="cmd">::math::statistics::mv-wls</b> <i class="arg">wt1</i> <i class="arg">weights_and_values</i></a></li>
<li><a href="#50"><b class="cmd">::math::statistics::mv-ols</b> <i class="arg">values</i></a></li>
<li><a href="#51"><b class="cmd">::math::statistics::pdf-normal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></li>
<li><a href="#52"><b class="cmd">::math::statistics::pdf-lognormal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></li>
<li><a href="#53"><b class="cmd">::math::statistics::pdf-exponential</b> <i class="arg">mean</i> <i class="arg">value</i></a></li>
<li><a href="#54"><b class="cmd">::math::statistics::pdf-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">value</i></a></li>
<li><a href="#55"><b class="cmd">::math::statistics::pdf-gamma</b> <i class="arg">alpha</i> <i class="arg">beta</i> <i class="arg">value</i></a></li>
<li><a href="#56"><b class="cmd">::math::statistics::pdf-poisson</b> <i class="arg">mu</i> <i class="arg">k</i></a></li>
<li><a href="#57"><b class="cmd">::math::statistics::pdf-chisquare</b> <i class="arg">df</i> <i class="arg">value</i></a></li>
<li><a href="#58"><b class="cmd">::math::statistics::pdf-student-t</b> <i class="arg">df</i> <i class="arg">value</i></a></li>
<li><a href="#59"><b class="cmd">::math::statistics::pdf-gamma</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">value</i></a></li>
<li><a href="#60"><b class="cmd">::math::statistics::pdf-beta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">value</i></a></li>
<li><a href="#61"><b class="cmd">::math::statistics::pdf-weibull</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></li>
<li><a href="#62"><b class="cmd">::math::statistics::pdf-gumbel</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></li>
<li><a href="#63"><b class="cmd">::math::statistics::pdf-pareto</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></li>
<li><a href="#64"><b class="cmd">::math::statistics::pdf-cauchy</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></li>
<li><a href="#65"><b class="cmd">::math::statistics::cdf-normal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></li>
<li><a href="#66"><b class="cmd">::math::statistics::cdf-lognormal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></li>
<li><a href="#67"><b class="cmd">::math::statistics::cdf-exponential</b> <i class="arg">mean</i> <i class="arg">value</i></a></li>
<li><a href="#68"><b class="cmd">::math::statistics::cdf-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">value</i></a></li>
<li><a href="#69"><b class="cmd">::math::statistics::cdf-students-t</b> <i class="arg">degrees</i> <i class="arg">value</i></a></li>
<li><a href="#70"><b class="cmd">::math::statistics::cdf-gamma</b> <i class="arg">alpha</i> <i class="arg">beta</i> <i class="arg">value</i></a></li>
<li><a href="#71"><b class="cmd">::math::statistics::cdf-poisson</b> <i class="arg">mu</i> <i class="arg">k</i></a></li>
<li><a href="#72"><b class="cmd">::math::statistics::cdf-beta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">value</i></a></li>
<li><a href="#73"><b class="cmd">::math::statistics::cdf-weibull</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></li>
<li><a href="#74"><b class="cmd">::math::statistics::cdf-gumbel</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></li>
<li><a href="#75"><b class="cmd">::math::statistics::cdf-pareto</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></li>
<li><a href="#76"><b class="cmd">::math::statistics::cdf-cauchy</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></li>
<li><a href="#77"><b class="cmd">::math::statistics::cdf-F</b> <i class="arg">nf1</i> <i class="arg">nf2</i> <i class="arg">value</i></a></li>
<li><a href="#78"><b class="cmd">::math::statistics::empirical-distribution</b> <i class="arg">values</i></a></li>
<li><a href="#79"><b class="cmd">::math::statistics::random-normal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">number</i></a></li>
<li><a href="#80"><b class="cmd">::math::statistics::random-lognormal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">number</i></a></li>
<li><a href="#81"><b class="cmd">::math::statistics::random-exponential</b> <i class="arg">mean</i> <i class="arg">number</i></a></li>
<li><a href="#82"><b class="cmd">::math::statistics::random-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">number</i></a></li>
<li><a href="#83"><b class="cmd">::math::statistics::random-gamma</b> <i class="arg">alpha</i> <i class="arg">beta</i> <i class="arg">number</i></a></li>
<li><a href="#84"><b class="cmd">::math::statistics::random-poisson</b> <i class="arg">mu</i> <i class="arg">number</i></a></li>
<li><a href="#85"><b class="cmd">::math::statistics::random-chisquare</b> <i class="arg">df</i> <i class="arg">number</i></a></li>
<li><a href="#86"><b class="cmd">::math::statistics::random-student-t</b> <i class="arg">df</i> <i class="arg">number</i></a></li>
<li><a href="#87"><b class="cmd">::math::statistics::random-beta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">number</i></a></li>
<li><a href="#88"><b class="cmd">::math::statistics::random-weibull</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">number</i></a></li>
<li><a href="#89"><b class="cmd">::math::statistics::random-gumbel</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">number</i></a></li>
<li><a href="#90"><b class="cmd">::math::statistics::random-pareto</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">number</i></a></li>
<li><a href="#91"><b class="cmd">::math::statistics::random-cauchy</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">number</i></a></li>
<li><a href="#92"><b class="cmd">::math::statistics::histogram-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">limits</i> <i class="arg">number</i></a></li>
<li><a href="#93"><b class="cmd">::math::statistics::incompleteGamma</b> <i class="arg">x</i> <i class="arg">p</i> <span class="opt">?tol?</span></a></li>
<li><a href="#94"><b class="cmd">::math::statistics::incompleteBeta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">x</i> <span class="opt">?tol?</span></a></li>
<li><a href="#95"><b class="cmd">::math::statistics::estimate-pareto</b> <i class="arg">values</i></a></li>
<li><a href="#96"><b class="cmd">::math::statistics::filter</b> <i class="arg">varname</i> <i class="arg">data</i> <i class="arg">expression</i></a></li>
<li><a href="#97"><b class="cmd">::math::statistics::map</b> <i class="arg">varname</i> <i class="arg">data</i> <i class="arg">expression</i></a></li>
<li><a href="#98"><b class="cmd">::math::statistics::samplescount</b> <i class="arg">varname</i> <i class="arg">list</i> <i class="arg">expression</i></a></li>
<li><a href="#99"><b class="cmd">::math::statistics::subdivide</b></a></li>
<li><a href="#100"><b class="cmd">::math::statistics::plot-scale</b> <i class="arg">canvas</i> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">ymin</i> <i class="arg">ymax</i></a></li>
<li><a href="#101"><b class="cmd">::math::statistics::plot-xydata</b> <i class="arg">canvas</i> <i class="arg">xdata</i> <i class="arg">ydata</i> <i class="arg">tag</i></a></li>
<li><a href="#102"><b class="cmd">::math::statistics::plot-xyline</b> <i class="arg">canvas</i> <i class="arg">xdata</i> <i class="arg">ydata</i> <i class="arg">tag</i></a></li>
<li><a href="#103"><b class="cmd">::math::statistics::plot-tdata</b> <i class="arg">canvas</i> <i class="arg">tdata</i> <i class="arg">tag</i></a></li>
<li><a href="#104"><b class="cmd">::math::statistics::plot-tline</b> <i class="arg">canvas</i> <i class="arg">tdata</i> <i class="arg">tag</i></a></li>
<li><a href="#105"><b class="cmd">::math::statistics::plot-histogram</b> <i class="arg">canvas</i> <i class="arg">counts</i> <i class="arg">limits</i> <i class="arg">tag</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>The <b class="package">math::statistics</b> package contains functions and procedures for
basic statistical data analysis, such as:</p>
<ul class="doctools_itemized">

<dt>list <i class="arg">data</i></dt>
<dd><p>List of values to chose from</p></dd>
<dt>int <i class="arg">sampleSize</i></dt>
<dd><p>Number of values per sample</p></dd>
<dt>int <i class="arg">numberSamples</i></dt>
<dd><p>Number of samples (default: 1)</p></dd>
</dl></dd>
<dt><a name="44"><b class="cmd">::math::statistics::wasserstein-distance</b> <i class="arg">prob1</i> <i class="arg">prob2</i></a></dt>
<dd><p>Compute the Wasserstein distance or earth mover's distance for two equidstantly spaced histograms
or probability densities. The histograms need not to be normalised to sum to one,
but they must have the same number of entries.</p>
<p>Note: the histograms are assumed to be based on the same equidistant intervals.
As the bounds are not passed, the value is expressed in the length of the intervals.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">prob1</i></dt>
<dd><p>List of values for the first histogram/probability density</p></dd>
<dt>list <i class="arg">prob2</i></dt>
<dd><p>List of values for the second histogram/probability density</p></dd>
</dl></dd>
<dt><a name="45"><b class="cmd">::math::statistics::kl-divergence</b> <i class="arg">prob1</i> <i class="arg">prob2</i></a></dt>
<dd><p>Compute the Kullback-Leibler (KL) divergence for two equidstantly spaced histograms
or probability densities. The histograms need not to be normalised to sum to one,
but they must have the same number of entries.</p>
<p>Note: the histograms are assumed to be based on the same equidistant intervals.
As the bounds are not passed, the value is expressed in the length of the intervals.</p>
<p>Note also that the KL divergence is not symmetric and that the second histogram
should not contain zeroes in places where the first histogram has non-zero values.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">prob1</i></dt>
<dd><p>List of values for the first histogram/probability density</p></dd>
<dt>list <i class="arg">prob2</i></dt>
<dd><p>List of values for the second histogram/probability density</p></dd>
</dl></dd>
<dt><a name="46"><b class="cmd">::math::statistics::logistic-model</b> <i class="arg">xdata</i> <i class="arg">ydata</i></a></dt>
<dd><p>Estimate the coefficients of the logistic model that fits the data best. The data consist
of independent x-values and the outcome 0 or 1 for each of the x-values. The result
can be used to estimate the probability that a certain x-value gives 1.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">xdata</i></dt>
<dd><p>List of values for which the success (1) or failure (0) is known</p></dd>
<dt>list <i class="arg">ydata</i></dt>
<dd><p>List of successes or failures corresponding to each value in <i class="term">xdata</i>.</p></dd>
</dl></dd>
<dt><a name="47"><b class="cmd">::math::statistics::logistic-probability</b> <i class="arg">coeffs</i> <i class="arg">x</i></a></dt>
<dd><p>Calculate the probability of success for the value <i class="term">x</i> given the coefficients of the
logistic model.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">coeffs</i></dt>
<dd><p>List of coefficients as determine by the <b class="cmd">logistic-model</b> command</p></dd>
<dt>float <i class="arg">x</i></dt>
<dd><p>X-value for which the probability needs to be determined</p></dd>
</dl></dd>
</dl>
</div>
<div id="section3" class="doctools_section"><h2><a name="section3">MULTIVARIATE LINEAR REGRESSION</a></h2>
<p>Besides the linear regression with a single independent variable, the
statistics package provides two procedures for doing ordinary
least squares (OLS) and weighted least squares (WLS) linear regression
with several variables. They were written by Eric Kemp-Benedict.</p>
<p>In addition to these two, it provides a procedure (tstat)
for calculating the value of the t-statistic for the specified number of
degrees of freedom that is required to demonstrate a given level of
significance.</p>
<p>Note: These procedures depend on the math::linearalgebra package.</p>
<p><em>Description of the procedures</em></p>
<dl class="doctools_definitions">
<dt><a name="48"><b class="cmd">::math::statistics::tstat</b> <i class="arg">dof</i> <span class="opt">?alpha?</span></a></dt>
<dd><p>Returns the value of the t-distribution t* satisfying</p>
<pre class="doctools_example">
    P(t*)  =  1 - alpha/2
    P(-t*) =  alpha/2
</pre>
<p>for the number of degrees of freedom dof.</p>
<p>Given a sample of normally-distributed data x, with an

the given confidence level.</p>
<dl class="doctools_arguments">
<dt>int <i class="arg">dof</i></dt>
<dd><p>Number of degrees of freedom</p></dd>
<dt>float <i class="arg">alpha</i></dt>
<dd><p>Confidence level of the t-distribution. Defaults to 0.05.</p></dd>
</dl></dd>
<dt><a name="49"><b class="cmd">::math::statistics::mv-wls</b> <i class="arg">wt1</i> <i class="arg">weights_and_values</i></a></dt>
<dd><p>Carries out a weighted least squares linear regression for
the data points provided, with weights assigned to each point.</p>
<p>The linear model is of the form</p>
<pre class="doctools_example">
    y = b0 + b1 * x1 + b2 * x2 ... + bN * xN + error
</pre>
<p>and each point satisfies</p>

<dt>list <i class="arg">weights_and_values</i></dt>
<dd><p>A list consisting of: the weight for the first observation, the data
for the first observation (as a sublist), the weight for the second
observation (as a sublist) and so on. The sublists of data are organised
as lists of the value of the dependent variable y and the independent
variables x1, x2 to xN.</p></dd>
</dl></dd>
<dt><a name="50"><b class="cmd">::math::statistics::mv-ols</b> <i class="arg">values</i></a></dt>
<dd><p>Carries out an ordinary least squares linear regression for
the data points provided.</p>
<p>This procedure simply calls ::mvlinreg::wls with the weights
set to 1.0, and returns the same information.</p></dd>
</dl>
<p><em>Example of the use:</em></p>
<pre class="doctools_example">

<li><p>The cumulative density (cdf-*)</p></li>
<li><p>Quantiles for the given distribution (quantiles-*)</p></li>
<li><p>Histograms for the given distribution (histogram-*)</p></li>
<li><p>List of random values with the given distribution (random-*)</p></li>
</ul>
<p>The following procedures have been implemented:</p>
<dl class="doctools_definitions">
<dt><a name="51"><b class="cmd">::math::statistics::pdf-normal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a normal distribution with
given mean and standard deviation.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">stdev</i></dt>
<dd><p>- Standard deviation of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="52"><b class="cmd">::math::statistics::pdf-lognormal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a log-normal distribution with
given mean and standard deviation.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">stdev</i></dt>
<dd><p>- Standard deviation of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="53"><b class="cmd">::math::statistics::pdf-exponential</b> <i class="arg">mean</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for an exponential
distribution with given mean.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="54"><b class="cmd">::math::statistics::pdf-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a uniform
distribution with given extremes.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum value of the distribution</p></dd>
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Maximum value of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="55"><b class="cmd">::math::statistics::pdf-gamma</b> <i class="arg">alpha</i> <i class="arg">beta</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Gamma
distribution with given shape and rate parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">alpha</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">beta</i></dt>
<dd><p>- Rate parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="56"><b class="cmd">::math::statistics::pdf-poisson</b> <i class="arg">mu</i> <i class="arg">k</i></a></dt>
<dd><p>Return the probability of a given number of occurrences in the same
interval (k) for a Poisson distribution with given mean (mu)</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mu</i></dt>
<dd><p>- Mean number of occurrences</p></dd>
<dt>int <i class="arg">k</i></dt>
<dd><p>- Number of occurences</p></dd>
</dl></dd>
<dt><a name="57"><b class="cmd">::math::statistics::pdf-chisquare</b> <i class="arg">df</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a chi square
distribution with given degrees of freedom</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">df</i></dt>
<dd><p>- Degrees of freedom</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="58"><b class="cmd">::math::statistics::pdf-student-t</b> <i class="arg">df</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Student's t
distribution with given degrees of freedom</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">df</i></dt>
<dd><p>- Degrees of freedom</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="59"><b class="cmd">::math::statistics::pdf-gamma</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Gamma
distribution with given shape and rate parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">a</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">b</i></dt>
<dd><p>- Rate parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="60"><b class="cmd">::math::statistics::pdf-beta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Beta
distribution with given shape parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">a</i></dt>
<dd><p>- First shape parameter</p></dd>
<dt>float <i class="arg">b</i></dt>
<dd><p>- Second shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="61"><b class="cmd">::math::statistics::pdf-weibull</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Weibull
distribution with given scale and shape parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="62"><b class="cmd">::math::statistics::pdf-gumbel</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Gumbel
distribution with given location and shape parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Location parameter</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="63"><b class="cmd">::math::statistics::pdf-pareto</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Pareto
distribution with given scale and shape parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">shape</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="64"><b class="cmd">::math::statistics::pdf-cauchy</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Cauchy
distribution with given location and shape parameters. Note that the Cauchy distribution
has no finite higher-order moments.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Location parameter</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="65"><b class="cmd">::math::statistics::cdf-normal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a normal
distribution with given mean and standard deviation, that is the
probability for values up to the given one.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">stdev</i></dt>
<dd><p>- Standard deviation of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="66"><b class="cmd">::math::statistics::cdf-lognormal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a log-normal
distribution with given mean and standard deviation, that is the
probability for values up to the given one.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">stdev</i></dt>
<dd><p>- Standard deviation of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="67"><b class="cmd">::math::statistics::cdf-exponential</b> <i class="arg">mean</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for an exponential
distribution with given mean.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="68"><b class="cmd">::math::statistics::cdf-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a uniform
distribution with given extremes.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum value of the distribution</p></dd>
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Maximum value of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="69"><b class="cmd">::math::statistics::cdf-students-t</b> <i class="arg">degrees</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Student's t
distribution with given number of degrees.</p>
<dl class="doctools_arguments">
<dt>int <i class="arg">degrees</i></dt>
<dd><p>- Number of degrees of freedom</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="70"><b class="cmd">::math::statistics::cdf-gamma</b> <i class="arg">alpha</i> <i class="arg">beta</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Gamma
distribution with given shape and rate parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">alpha</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">beta</i></dt>
<dd><p>- Rate parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the cumulative probability is required</p></dd>
</dl></dd>
<dt><a name="71"><b class="cmd">::math::statistics::cdf-poisson</b> <i class="arg">mu</i> <i class="arg">k</i></a></dt>
<dd><p>Return the cumulative probability of a given number of occurrences in
the same interval (k) for a Poisson distribution with given mean (mu).</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mu</i></dt>
<dd><p>- Mean number of occurrences</p></dd>
<dt>int <i class="arg">k</i></dt>
<dd><p>- Number of occurences</p></dd>
</dl></dd>
<dt><a name="72"><b class="cmd">::math::statistics::cdf-beta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Beta
distribution with given shape parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">a</i></dt>
<dd><p>- First shape parameter</p></dd>
<dt>float <i class="arg">b</i></dt>
<dd><p>- Second shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="73"><b class="cmd">::math::statistics::cdf-weibull</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Weibull
distribution with given scale and shape parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">shape</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="74"><b class="cmd">::math::statistics::cdf-gumbel</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Gumbel
distribution with given location and scale parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Location parameter</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="75"><b class="cmd">::math::statistics::cdf-pareto</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Pareto
distribution with given scale and shape parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">shape</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="76"><b class="cmd">::math::statistics::cdf-cauchy</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Cauchy
distribution with given location and scale parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Location parameter</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="77"><b class="cmd">::math::statistics::cdf-F</b> <i class="arg">nf1</i> <i class="arg">nf2</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for an F
distribution with nf1 and nf2 degrees of freedom.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">nf1</i></dt>
<dd><p>- Degrees of freedom for the numerator</p></dd>
<dt>float <i class="arg">nf2</i></dt>
<dd><p>- Degrees of freedom for the denominator</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="78"><b class="cmd">::math::statistics::empirical-distribution</b> <i class="arg">values</i></a></dt>
<dd><p>Return a list of values and their empirical probability. The values are sorted in increasing order.
(The implementation follows the description at the corresponding Wikipedia page)</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">values</i></dt>
<dd><p>- List of data to be examined</p></dd>
</dl></dd>
<dt><a name="79"><b class="cmd">::math::statistics::random-normal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying a normal
distribution with given mean and standard deviation.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">stdev</i></dt>
<dd><p>- Standard deviation of the distribution</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="80"><b class="cmd">::math::statistics::random-lognormal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying a log-normal
distribution with given mean and standard deviation.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">stdev</i></dt>
<dd><p>- Standard deviation of the distribution</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="81"><b class="cmd">::math::statistics::random-exponential</b> <i class="arg">mean</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying an exponential
distribution with given mean.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="82"><b class="cmd">::math::statistics::random-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying a uniform
distribution with given extremes.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum value of the distribution</p></dd>
<dt>float <i class="arg">xmax</i></dt>
<dd><p>- Maximum value of the distribution</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="83"><b class="cmd">::math::statistics::random-gamma</b> <i class="arg">alpha</i> <i class="arg">beta</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Gamma distribution with given shape and rate parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">alpha</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">beta</i></dt>
<dd><p>- Rate parameter</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="84"><b class="cmd">::math::statistics::random-poisson</b> <i class="arg">mu</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Poisson distribution with given mean.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mu</i></dt>
<dd><p>- Mean of the distribution</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="85"><b class="cmd">::math::statistics::random-chisquare</b> <i class="arg">df</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a chi square distribution with given degrees of freedom.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">df</i></dt>
<dd><p>- Degrees of freedom</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="86"><b class="cmd">::math::statistics::random-student-t</b> <i class="arg">df</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Student's t distribution with given degrees of freedom.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">df</i></dt>
<dd><p>- Degrees of freedom</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="87"><b class="cmd">::math::statistics::random-beta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Beta distribution with given shape parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">a</i></dt>
<dd><p>- First shape parameter</p></dd>
<dt>float <i class="arg">b</i></dt>
<dd><p>- Second shape parameter</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="88"><b class="cmd">::math::statistics::random-weibull</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Weibull distribution with given scale and shape parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">shape</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="89"><b class="cmd">::math::statistics::random-gumbel</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Gumbel distribution with given location and scale parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Location parameter</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="90"><b class="cmd">::math::statistics::random-pareto</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Pareto distribution with given scale and shape parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">shape</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="91"><b class="cmd">::math::statistics::random-cauchy</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Cauchy distribution with given location and scale parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Location parameter</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="92"><b class="cmd">::math::statistics::histogram-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">limits</i> <i class="arg">number</i></a></dt>
<dd><p>Return the expected histogram for a uniform distribution.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum value of the distribution</p></dd>
<dt>float <i class="arg">xmax</i></dt>
<dd><p>- Maximum value of the distribution</p></dd>
<dt>list <i class="arg">limits</i></dt>
<dd><p>- Upper limits for the buckets in the histogram</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Total number of &quot;observations&quot; in the histogram</p></dd>
</dl></dd>
<dt><a name="93"><b class="cmd">::math::statistics::incompleteGamma</b> <i class="arg">x</i> <i class="arg">p</i> <span class="opt">?tol?</span></a></dt>
<dd><p>Evaluate the incomplete Gamma integral</p>
<pre class="doctools_example">
                    1       / x               p-1
      P(p,x) =  --------   |   dt exp(-t) * t
                Gamma(p)  / 0
</pre>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>- Value of x (limit of the integral)</p></dd>
<dt>float <i class="arg">p</i></dt>
<dd><p>- Value of p in the integrand</p></dd>
<dt>float <i class="arg">tol</i></dt>
<dd><p>- Required tolerance (default: 1.0e-9)</p></dd>
</dl></dd>
<dt><a name="94"><b class="cmd">::math::statistics::incompleteBeta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">x</i> <span class="opt">?tol?</span></a></dt>
<dd><p>Evaluate the incomplete Beta integral</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">a</i></dt>
<dd><p>- First shape parameter</p></dd>
<dt>float <i class="arg">b</i></dt>
<dd><p>- Second shape parameter</p></dd>
<dt>float <i class="arg">x</i></dt>
<dd><p>- Value of x (limit of the integral)</p></dd>
<dt>float <i class="arg">tol</i></dt>
<dd><p>- Required tolerance (default: 1.0e-9)</p></dd>
</dl></dd>
<dt><a name="95"><b class="cmd">::math::statistics::estimate-pareto</b> <i class="arg">values</i></a></dt>
<dd><p>Estimate the parameters for the Pareto distribution that comes closest to the given values.
Returns the estimated scale and shape parameters, as well as the standard error for the shape parameter.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">values</i></dt>
<dd><p>- List of values, assumed to be distributed according to a Pareto distribution</p></dd>
</dl></dd>
</dl>
<p>TO DO: more function descriptions to be added</p>
</div>
<div id="section5" class="doctools_section"><h2><a name="section5">DATA MANIPULATION</a></h2>
<p>The data manipulation procedures act on lists or lists of lists:</p>
<dl class="doctools_definitions">
<dt><a name="96"><b class="cmd">::math::statistics::filter</b> <i class="arg">varname</i> <i class="arg">data</i> <i class="arg">expression</i></a></dt>
<dd><p>Return a list consisting of the data for which the logical
expression is true (this command works analogously to the command <b class="cmd"><a href="../../../../index.html#foreach">foreach</a></b>).</p>
<dl class="doctools_arguments">
<dt>string <i class="arg">varname</i></dt>
<dd><p>- Name of the variable used in the expression</p></dd>
<dt>list <i class="arg">data</i></dt>
<dd><p>- List of data</p></dd>
<dt>string <i class="arg">expression</i></dt>
<dd><p>- Logical expression using the variable name</p></dd>
</dl></dd>
<dt><a name="97"><b class="cmd">::math::statistics::map</b> <i class="arg">varname</i> <i class="arg">data</i> <i class="arg">expression</i></a></dt>
<dd><p>Return a list consisting of the data that are transformed via the
expression.</p>
<dl class="doctools_arguments">
<dt>string <i class="arg">varname</i></dt>
<dd><p>- Name of the variable used in the expression</p></dd>
<dt>list <i class="arg">data</i></dt>
<dd><p>- List of data</p></dd>
<dt>string <i class="arg">expression</i></dt>
<dd><p>- Expression to be used to transform (map) the data</p></dd>
</dl></dd>
<dt><a name="98"><b class="cmd">::math::statistics::samplescount</b> <i class="arg">varname</i> <i class="arg">list</i> <i class="arg">expression</i></a></dt>
<dd><p>Return a list consisting of the <i class="term">counts</i> of all data in the
sublists of the &quot;list&quot; argument for which the expression is true.</p>
<dl class="doctools_arguments">
<dt>string <i class="arg">varname</i></dt>
<dd><p>- Name of the variable used in the expression</p></dd>
<dt>list <i class="arg">data</i></dt>
<dd><p>- List of sublists, each containing the data</p></dd>
<dt>string <i class="arg">expression</i></dt>
<dd><p>- Logical expression to test the data (defaults to
&quot;true&quot;).</p></dd>
</dl></dd>
<dt><a name="99"><b class="cmd">::math::statistics::subdivide</b></a></dt>
<dd><p>Routine <em>PM</em> - not implemented yet</p></dd>
</dl>
</div>
<div id="section6" class="doctools_section"><h2><a name="section6">PLOT PROCEDURES</a></h2>
<p>The following simple plotting procedures are available:</p>
<dl class="doctools_definitions">
<dt><a name="100"><b class="cmd">::math::statistics::plot-scale</b> <i class="arg">canvas</i> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">ymin</i> <i class="arg">ymax</i></a></dt>
<dd><p>Set the scale for a plot in the given canvas. All plot routines expect
this function to be called first. There is no automatic scaling
provided.</p>
<dl class="doctools_arguments">
<dt>widget <i class="arg">canvas</i></dt>
<dd><p>- Canvas widget to use</p></dd>
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum x value</p></dd>
<dt>float <i class="arg">xmax</i></dt>
<dd><p>- Maximum x value</p></dd>
<dt>float <i class="arg">ymin</i></dt>
<dd><p>- Minimum y value</p></dd>
<dt>float <i class="arg">ymax</i></dt>
<dd><p>- Maximum y value</p></dd>
</dl></dd>
<dt><a name="101"><b class="cmd">::math::statistics::plot-xydata</b> <i class="arg">canvas</i> <i class="arg">xdata</i> <i class="arg">ydata</i> <i class="arg">tag</i></a></dt>
<dd><p>Create a simple XY plot in the given canvas - the data are
shown as a collection of dots. The tag can be used to manipulate the
appearance.</p>
<dl class="doctools_arguments">
<dt>widget <i class="arg">canvas</i></dt>
<dd><p>- Canvas widget to use</p></dd>
<dt>float <i class="arg">xdata</i></dt>
<dd><p>- Series of independent data</p></dd>
<dt>float <i class="arg">ydata</i></dt>
<dd><p>- Series of dependent data</p></dd>
<dt>string <i class="arg">tag</i></dt>
<dd><p>- Tag to give to the plotted data (defaults to xyplot)</p></dd>
</dl></dd>
<dt><a name="102"><b class="cmd">::math::statistics::plot-xyline</b> <i class="arg">canvas</i> <i class="arg">xdata</i> <i class="arg">ydata</i> <i class="arg">tag</i></a></dt>
<dd><p>Create a simple XY plot in the given canvas - the data are
shown as a line through the data points. The tag can be used to
manipulate the appearance.</p>
<dl class="doctools_arguments">
<dt>widget <i class="arg">canvas</i></dt>
<dd><p>- Canvas widget to use</p></dd>
<dt>list <i class="arg">xdata</i></dt>
<dd><p>- Series of independent data</p></dd>
<dt>list <i class="arg">ydata</i></dt>
<dd><p>- Series of dependent data</p></dd>
<dt>string <i class="arg">tag</i></dt>
<dd><p>- Tag to give to the plotted data (defaults to xyplot)</p></dd>
</dl></dd>
<dt><a name="103"><b class="cmd">::math::statistics::plot-tdata</b> <i class="arg">canvas</i> <i class="arg">tdata</i> <i class="arg">tag</i></a></dt>
<dd><p>Create a simple XY plot in the given canvas - the data are
shown as a collection of dots. The horizontal coordinate is equal to the
index. The tag can be used to manipulate the appearance.
This type of presentation is suitable for autocorrelation functions for
instance or for inspecting the time-dependent behaviour.</p>
<dl class="doctools_arguments">
<dt>widget <i class="arg">canvas</i></dt>
<dd><p>- Canvas widget to use</p></dd>
<dt>list <i class="arg">tdata</i></dt>
<dd><p>- Series of dependent data</p></dd>
<dt>string <i class="arg">tag</i></dt>
<dd><p>- Tag to give to the plotted data (defaults to xyplot)</p></dd>
</dl></dd>
<dt><a name="104"><b class="cmd">::math::statistics::plot-tline</b> <i class="arg">canvas</i> <i class="arg">tdata</i> <i class="arg">tag</i></a></dt>
<dd><p>Create a simple XY plot in the given canvas - the data are
shown as a line. See plot-tdata for an explanation.</p>
<dl class="doctools_arguments">
<dt>widget <i class="arg">canvas</i></dt>
<dd><p>- Canvas widget to use</p></dd>
<dt>list <i class="arg">tdata</i></dt>
<dd><p>- Series of dependent data</p></dd>
<dt>string <i class="arg">tag</i></dt>
<dd><p>- Tag to give to the plotted data (defaults to xyplot)</p></dd>
</dl></dd>
<dt><a name="105"><b class="cmd">::math::statistics::plot-histogram</b> <i class="arg">canvas</i> <i class="arg">counts</i> <i class="arg">limits</i> <i class="arg">tag</i></a></dt>
<dd><p>Create a simple histogram in the given canvas</p>
<dl class="doctools_arguments">
<dt>widget <i class="arg">canvas</i></dt>
<dd><p>- Canvas widget to use</p></dd>
<dt>list <i class="arg">counts</i></dt>
<dd><p>- Series of bucket counts</p></dd>
<dt>list <i class="arg">limits</i></dt>

<div class='fossil-doc' data-title='math::trig - Tcl Math Library'>
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<div class="doctools">
<h1 class="doctools_title">math::trig(n) 1.0.0 tcllib &quot;Tcl Math Library&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>math::trig - Trigonometric anf hyperbolic functions</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">FUNCTIONS</a></li>
<li class="doctools_section"><a href="#section3">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.5</b></li>
<li>package require <b class="pkgname">math::trig 1.0.0</b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::math::trig::radian_reduced</b> <i class="arg">angle</i></a></li>
<li><a href="#2"><b class="cmd">::math::trig::degree_reduced</b> <i class="arg">angle</i></a></li>
<li><a href="#3"><b class="cmd">::math::trig::cosec</b> <i class="arg">angle</i></a></li>
<li><a href="#4"><b class="cmd">::math::trig::sec</b> <i class="arg">angle</i></a></li>
<li><a href="#5"><b class="cmd">::math::trig::cotan</b> <i class="arg">angle</i></a></li>
<li><a href="#6"><b class="cmd">::math::trig::acosec</b> <i class="arg">value</i></a></li>
<li><a href="#7"><b class="cmd">::math::trig::asec</b> <i class="arg">value</i></a></li>
<li><a href="#8"><b class="cmd">::math::trig::acotan</b> <i class="arg">value</i></a></li>
<li><a href="#9"><b class="cmd">::math::trig::cosech</b> <i class="arg">value</i></a></li>
<li><a href="#10"><b class="cmd">::math::trig::sech</b> <i class="arg">value</i></a></li>
<li><a href="#11"><b class="cmd">::math::trig::cotanh</b> <i class="arg">value</i></a></li>
<li><a href="#12"><b class="cmd">::math::trig::asinh</b> <i class="arg">value</i></a></li>
<li><a href="#13"><b class="cmd">::math::trig::acosh</b> <i class="arg">value</i></a></li>
<li><a href="#14"><b class="cmd">::math::trig::atanh</b> <i class="arg">value</i></a></li>
<li><a href="#15"><b class="cmd">::math::trig::acosech</b> <i class="arg">value</i></a></li>
<li><a href="#16"><b class="cmd">::math::trig::asech</b> <i class="arg">value</i></a></li>
<li><a href="#17"><b class="cmd">::math::trig::acotanh</b> <i class="arg">value</i></a></li>
<li><a href="#18"><b class="cmd">::math::trig::sind</b> <i class="arg">angle</i></a></li>
<li><a href="#19"><b class="cmd">::math::trig::cosd</b> <i class="arg">angle</i></a></li>
<li><a href="#20"><b class="cmd">::math::trig::tand</b> <i class="arg">angle</i></a></li>
<li><a href="#21"><b class="cmd">::math::trig::cosecd</b> <i class="arg">angle</i></a></li>
<li><a href="#22"><b class="cmd">::math::trig::secd</b> <i class="arg">angle</i></a></li>
<li><a href="#23"><b class="cmd">::math::trig::cotand</b> <i class="arg">angle</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>The <i class="term">math::trig</i> package defines a set of trigonomic and hyperbolic functions
and their inverses. In addition it defines versions of the trigonomic functions
that take arguments in degrees instead of radians.</p>
<p>For easy use these functions may be imported into the <i class="term">tcl::mathfunc</i> namespace,
so that they can be used directly in the <i class="term">expr</i> command.</p>
</div>
<div id="section2" class="doctools_section"><h2><a name="section2">FUNCTIONS</a></h2>
<p>The functions <i class="term">radian_reduced</i> and <i class="term">degree_reduced</i> return a reduced angle, in
respectively radians and degrees, in the intervals [0, 2pi) and [0, 360):</p>
<dl class="doctools_definitions">
<dt><a name="1"><b class="cmd">::math::trig::radian_reduced</b> <i class="arg">angle</i></a></dt>
<dd><p>Return the equivalent angle in the interval [0, 2pi).</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">angle</i></dt>
<dd><p>Angle (in radians)</p></dd>
</dl></dd>
<dt><a name="2"><b class="cmd">::math::trig::degree_reduced</b> <i class="arg">angle</i></a></dt>
<dd><p>Return the equivalent angle in the interval [0, 360).</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">angle</i></dt>
<dd><p>Angle (in degrees)</p></dd>
</dl></dd>
</dl>
<p>The following trigonomic functions are defined in addition to the ones defined
in the <i class="term">expr</i> command:</p>
<dl class="doctools_definitions">
<dt><a name="3"><b class="cmd">::math::trig::cosec</b> <i class="arg">angle</i></a></dt>
<dd><p>Calculate the cosecant of the angle (1/cos(angle))</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">angle</i></dt>
<dd><p>Angle (in radians)</p></dd>
</dl></dd>
<dt><a name="4"><b class="cmd">::math::trig::sec</b> <i class="arg">angle</i></a></dt>
<dd><p>Calculate the secant of the angle (1/sin(angle))</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">angle</i></dt>
<dd><p>Angle (in radians)</p></dd>
</dl></dd>
<dt><a name="5"><b class="cmd">::math::trig::cotan</b> <i class="arg">angle</i></a></dt>
<dd><p>Calculate the cotangent of the angle (1/tan(angle))</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">angle</i></dt>
<dd><p>Angle (in radians)</p></dd>
</dl></dd>
</dl>
<p>For these functions also the inverses are defined:</p>
<dl class="doctools_definitions">
<dt><a name="6"><b class="cmd">::math::trig::acosec</b> <i class="arg">value</i></a></dt>
<dd><p>Calculate the arc cosecant of the value</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">value</i></dt>
<dd><p>Value of the argument</p></dd>
</dl></dd>
<dt><a name="7"><b class="cmd">::math::trig::asec</b> <i class="arg">value</i></a></dt>
<dd><p>Calculate the arc secant of the value</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">value</i></dt>
<dd><p>Value of the argument</p></dd>
</dl></dd>
<dt><a name="8"><b class="cmd">::math::trig::acotan</b> <i class="arg">value</i></a></dt>
<dd><p>Calculate the arc cotangent of the value</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">value</i></dt>
<dd><p>Value of the argument</p></dd>
</dl></dd>
</dl>
<p>The following hyperbolic and inverse hyperbolic functions are defined:</p>
<dl class="doctools_definitions">
<dt><a name="9"><b class="cmd">::math::trig::cosech</b> <i class="arg">value</i></a></dt>
<dd><p>Calculate the hyperbolic cosecant of the value (1/sinh(value))</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">value</i></dt>
<dd><p>Value of the argument</p></dd>
</dl></dd>
<dt><a name="10"><b class="cmd">::math::trig::sech</b> <i class="arg">value</i></a></dt>
<dd><p>Calculate the hyperbolic secant of the value (1/cosh(value))</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">value</i></dt>
<dd><p>Value of the argument</p></dd>
</dl></dd>
<dt><a name="11"><b class="cmd">::math::trig::cotanh</b> <i class="arg">value</i></a></dt>
<dd><p>Calculate the hyperbolic cotangent of the value (1/tanh(value))</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">value</i></dt>
<dd><p>Value of the argument</p></dd>
</dl></dd>
<dt><a name="12"><b class="cmd">::math::trig::asinh</b> <i class="arg">value</i></a></dt>
<dd><p>Calculate the arc hyperbolic sine of the value</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">value</i></dt>
<dd><p>Value of the argument</p></dd>
</dl></dd>
<dt><a name="13"><b class="cmd">::math::trig::acosh</b> <i class="arg">value</i></a></dt>
<dd><p>Calculate the arc hyperbolic cosine of the value</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">value</i></dt>
<dd><p>Value of the argument</p></dd>
</dl></dd>
<dt><a name="14"><b class="cmd">::math::trig::atanh</b> <i class="arg">value</i></a></dt>
<dd><p>Calculate the arc hyperbolic tangent of the value</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">value</i></dt>
<dd><p>Value of the argument</p></dd>
</dl></dd>
<dt><a name="15"><b class="cmd">::math::trig::acosech</b> <i class="arg">value</i></a></dt>
<dd><p>Calculate the arc hyperbolic cosecant of the value</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">value</i></dt>
<dd><p>Value of the argument</p></dd>
</dl></dd>
<dt><a name="16"><b class="cmd">::math::trig::asech</b> <i class="arg">value</i></a></dt>
<dd><p>Calculate the arc hyperbolic secant of the value</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">value</i></dt>
<dd><p>Value of the argument</p></dd>
</dl></dd>
<dt><a name="17"><b class="cmd">::math::trig::acotanh</b> <i class="arg">value</i></a></dt>
<dd><p>Calculate the arc hyperbolic cotangent of the value</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">value</i></dt>
<dd><p>Value of the argument</p></dd>
</dl></dd>
</dl>
<p>The following versions of the common trigonometric functions and their
inverses are defined:</p>
<dl class="doctools_definitions">
<dt><a name="18"><b class="cmd">::math::trig::sind</b> <i class="arg">angle</i></a></dt>
<dd><p>Calculate the sine of the angle (in degrees)</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">angle</i></dt>
<dd><p>Angle (in degrees)</p></dd>
</dl></dd>
<dt><a name="19"><b class="cmd">::math::trig::cosd</b> <i class="arg">angle</i></a></dt>
<dd><p>Calculate the cosine of the angle (in degrees)</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">angle</i></dt>
<dd><p>Angle (in radians)</p></dd>
</dl></dd>
<dt><a name="20"><b class="cmd">::math::trig::tand</b> <i class="arg">angle</i></a></dt>
<dd><p>Calculate the cotangent of the angle (in degrees)</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">angle</i></dt>
<dd><p>Angle (in degrees)</p></dd>
</dl></dd>
<dt><a name="21"><b class="cmd">::math::trig::cosecd</b> <i class="arg">angle</i></a></dt>
<dd><p>Calculate the cosecant of the angle (in degrees)</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">angle</i></dt>
<dd><p>Angle (in degrees)</p></dd>
</dl></dd>
<dt><a name="22"><b class="cmd">::math::trig::secd</b> <i class="arg">angle</i></a></dt>
<dd><p>Calculate the secant of the angle (in degrees)</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">angle</i></dt>
<dd><p>Angle (in degrees)</p></dd>
</dl></dd>
<dt><a name="23"><b class="cmd">::math::trig::cotand</b> <i class="arg">angle</i></a></dt>
<dd><p>Calculate the cotangent of the angle (in degrees)</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">angle</i></dt>
<dd><p>Angle (in degrees)</p></dd>
</dl></dd>
</dl>
</div>
<div id="section3" class="doctools_section"><h2><a name="section3">Bugs, Ideas, Feedback</a></h2>
<p>This document, and the package it describes, will undoubtedly contain
bugs and other problems.
Please report such in the category <em>math :: trig</em> of the
<a href="http://core.tcl.tk/tcllib/reportlist">Tcllib Trackers</a>.
Please also report any ideas for enhancements you may have for either
package and/or documentation.</p>
<p>When proposing code changes, please provide <em>unified diffs</em>,
i.e the output of <b class="const">diff -u</b>.</p>
<p>Note further that <em>attachments</em> are strongly preferred over
inlined patches. Attachments can be made by going to the <b class="const">Edit</b>
form of the ticket immediately after its creation, and then using the
left-most button in the secondary navigation bar.</p>
</div>
<div id="keywords" class="doctools_section"><h2><a name="keywords">Keywords</a></h2>
<p><a href="../../../../index.html#math">math</a>, <a href="../../../../index.html#trigonometry">trigonometry</a></p>
</div>
<div id="category" class="doctools_section"><h2><a name="category">Category</a></h2>
<p>Mathematics</p>
</div>
<div id="copyright" class="doctools_section"><h2><a name="copyright">Copyright</a></h2>
<p>Copyright &copy; 2018 Arjen Markus</p>
</div>
</div>

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<div class="doctools">
<h1 class="doctools_title">namespacex(n) 0.2 tcllib &quot;Namespace utility commands&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>namespacex - Namespace utility commands</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">Commands</a></li>
<li class="doctools_section"><a href="#section3">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.5</b></li>
<li>package require <b class="pkgname">namespacex <span class="opt">?0.2?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::namespacex hook add</b> <span class="opt">?<i class="arg">namespace</i>?</span> <i class="arg">cmdprefix</i></a></li>
<li><a href="#2"><b class="cmd">::namespacex hook proc</b> <span class="opt">?<i class="arg">namespace</i>?</span> <i class="arg">arguments</i> <i class="arg">body</i></a></li>
<li><a href="#3"><b class="cmd">::namespacex hook on</b> <span class="opt">?<i class="arg">namespace</i>?</span> <i class="arg">guardcmdprefix</i> <i class="arg">actioncmdprefix</i></a></li>
<li><a href="#4"><b class="cmd">::namespacex hook next</b> <i class="arg">arg</i>...</a></li>
<li><a href="#5"><b class="cmd">::namespacex import fromns</b> <i class="arg">cmdname <span class="opt">?<i class="arg">newname</i> ...?</span></i></a></li>
<li><a href="#6"><b class="cmd">::namespacex info allchildren</b> <i class="arg">namespace</i></a></li>
<li><a href="#7"><b class="cmd">::namespacex info allvars</b> <i class="arg">namespace</i></a></li>
<li><a href="#8"><b class="cmd">::namespacex normalize</b> <i class="arg">namespace</i></a></li>
<li><a href="#9"><b class="cmd">::namespacex info vars</b> <i class="arg">namespace</i> <span class="opt">?<i class="arg">pattern</i>?</span></a></li>
<li><a href="#10"><b class="cmd">::namespacex state get</b> <i class="arg">namespace</i></a></li>
<li><a href="#11"><b class="cmd">::namespacex state set</b> <i class="arg">namespace</i> <i class="arg">dict</i></a></li>
<li><a href="#12"><b class="cmd">::namespacex state drop</b> <i class="arg">namespace</i></a></li>
<li><a href="#13"><b class="cmd">::namespacex strip</b> <i class="arg">prefix</i> <i class="arg">namespaces</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>This package provides a number of utility commands for working with
namespaces.
The commands fall into four categories:</p>
<ol class="doctools_enumerated">
<li><p>Hook commands provide and manipulate a chain of commands which
replaces the single regular <b class="cmd"><a href="../../../../index.html#namespace_unknown">namespace unknown</a></b> handler.</p></li>
<li><p>An import command provides the ability to import any command
from another namespace.</p></li>
<li><p>Information commands allow querying of variables and child
namespaces.</p></li>
<li><p>State commands provide a means to serialize variable values in
a namespace.</p></li>
</ol>
</div>
<div id="section2" class="doctools_section"><h2><a name="section2">Commands</a></h2>
<dl class="doctools_definitions">
<dt><a name="1"><b class="cmd">::namespacex hook add</b> <span class="opt">?<i class="arg">namespace</i>?</span> <i class="arg">cmdprefix</i></a></dt>
<dd><p>Adds the <i class="arg">cmdprefix</i> to the chain of unknown command handlers that
are invoked when the <i class="arg">namespace</i> would otherwise invoke its
unknown handler.
If <i class="arg">namespace</i> is not specified, then <i class="arg">cmdprefix</i> is added to
the chain of handlers for the namespace of the caller.</p>
<p>The chain of <i class="arg">cmdprefix</i> are executed in reverse order of
addition, <em>i.e.</em> the most recently added <i class="arg">cmdprefix</i> is
executed first.
When executed, <i class="arg">cmdprefix</i> has additional arguments appended to it
as would any namespace unknown handler.</p></dd>
<dt><a name="2"><b class="cmd">::namespacex hook proc</b> <span class="opt">?<i class="arg">namespace</i>?</span> <i class="arg">arguments</i> <i class="arg">body</i></a></dt>
<dd><p>Adds an anonymous procedure to the chain of namespace unknown handlers
for the <i class="arg">namespace</i>.</p>
<p>If <i class="arg">namespace</i> is not specified, then the handler is added
to the chain of handlers for the namespace of the caller.</p>
<p>The <i class="arg">arguments</i> and <i class="arg">body</i> are specified as for the
core <b class="cmd"><a href="../../../../index.html#proc">proc</a></b> command.</p></dd>
<dt><a name="3"><b class="cmd">::namespacex hook on</b> <span class="opt">?<i class="arg">namespace</i>?</span> <i class="arg">guardcmdprefix</i> <i class="arg">actioncmdprefix</i></a></dt>
<dd><p>Adds a guarded action to the chain of namespace unknown handlers for
the <i class="arg">namespace</i>.</p>
<p>If <i class="arg">namespace</i> is not specified, then the handler is added
to the chain of handlers for the namespace of the caller.</p>
<p>The <i class="arg">guardcmdprefix</i> is executed first. If it returns a
value that can be interpreted as false, then the next unknown hander
in the chain is executed. Otherwise, <i class="arg">actioncmdprefix</i> is executed
and the return value of the handler is the value returned by
<i class="arg">actioncmdprefix</i>.</p>
<p>When executed, both <i class="arg">guardcmdprefix</i> and
<i class="arg">actioncmdprefix</i> have the same additional arguments appended as
for any namespace unknown handler.</p></dd>
<dt><a name="4"><b class="cmd">::namespacex hook next</b> <i class="arg">arg</i>...</a></dt>
<dd><p>This command is available to namespace hooks to execute the next hook
in the chain of handlers for the namespace.</p></dd>
<dt><a name="5"><b class="cmd">::namespacex import fromns</b> <i class="arg">cmdname <span class="opt">?<i class="arg">newname</i> ...?</span></i></a></dt>
<dd><p>Imports the command <i class="arg">cmdname</i> from the <i class="arg">fromns</i> namespace into
the namespace of the caller.
The <i class="arg">cmdname</i> command is imported even if the <i class="arg">fromns</i> did not
originally export the command.</p>
<p>If <i class="arg">newname</i> is specified, then the imported command will
be known by that name. Otherwise, the command retains is original name
as given by <i class="arg">cmdname</i>.</p>
<p>Additional pairs of <i class="arg">cmdname</i> / <i class="arg">newname</i> arguments may
also be specified.</p></dd>
<dt><a name="6"><b class="cmd">::namespacex info allchildren</b> <i class="arg">namespace</i></a></dt>
<dd><p>Returns a list containing the names of all child namespaces in the
specified <i class="arg">namespace</i> and its children. The names are all fully
qualified.</p></dd>
<dt><a name="7"><b class="cmd">::namespacex info allvars</b> <i class="arg">namespace</i></a></dt>
<dd><p>Returns a list containing the names of all variables in the specified
<i class="arg">namespace</i> and its children. The names are all given relative to
<i class="arg">namespace</i>, and <em>not</em> fully qualified.</p></dd>
<dt><a name="8"><b class="cmd">::namespacex normalize</b> <i class="arg">namespace</i></a></dt>
<dd><p>Returns the absolute name of <i class="arg">namespace</i>, which is resolved
relative to the namespace of the caller, with all unneeded colon
characters removed.</p></dd>
<dt><a name="9"><b class="cmd">::namespacex info vars</b> <i class="arg">namespace</i> <span class="opt">?<i class="arg">pattern</i>?</span></a></dt>
<dd><p>Returns a list containing the names of all variables in
the specified <i class="arg">namespace</i>.
If the <i class="arg">pattern</i> argument is specified, then only variables
matching <i class="arg">pattern</i> are returned. Matching is determined using the
same rules as for <b class="cmd">string match</b>.</p></dd>
<dt><a name="10"><b class="cmd">::namespacex state get</b> <i class="arg">namespace</i></a></dt>
<dd><p>Returns a dictionary holding the names and values of all variables in
the specified <i class="arg">namespace</i> and its child namespaces.</p>
<p>Note that the names are all relative to <i class="arg">namespace</i>, and
<em>not</em> fully qualified.</p></dd>
<dt><a name="11"><b class="cmd">::namespacex state set</b> <i class="arg">namespace</i> <i class="arg">dict</i></a></dt>
<dd><p>Takes a dictionary holding the names and values for a set of variables
and replaces the current state of the specified <i class="arg">namespace</i> and
its child namespaces with this state.
The result of the command is the empty string.</p></dd>
<dt><a name="12"><b class="cmd">::namespacex state drop</b> <i class="arg">namespace</i></a></dt>
<dd><p>Unsets all variables in the specified <i class="arg">namespace</i> and its child
namespaces.
The result of the command is the empty string.</p></dd>
<dt><a name="13"><b class="cmd">::namespacex strip</b> <i class="arg">prefix</i> <i class="arg">namespaces</i></a></dt>
<dd><p>Each item in <i class="arg">namespaces</i> must be the absolute normalized name of
a child namespace of namespace <i class="arg">prefix</i>.
Returns the corresponding list of relative names of child namespaces.</p></dd>
</dl>
</div>
<div id="section3" class="doctools_section"><h2><a name="section3">Bugs, Ideas, Feedback</a></h2>
<p>This document, and the package it describes, will undoubtedly contain
bugs and other problems.
Please report such in the category <em>namespacex</em> of the
<a href="http://core.tcl.tk/tcllib/reportlist">Tcllib Trackers</a>.
Please also report any ideas for enhancements you may have for either
package and/or documentation.</p>
<p>When proposing code changes, please provide <em>unified diffs</em>,
i.e the output of <b class="const">diff -u</b>.</p>
<p>Note further that <em>attachments</em> are strongly preferred over
inlined patches. Attachments can be made by going to the <b class="const">Edit</b>
form of the ticket immediately after its creation, and then using the
left-most button in the secondary navigation bar.</p>
</div>
<div id="keywords" class="doctools_section"><h2><a name="keywords">Keywords</a></h2>
<p><a href="../../../../index.html#extended_namespace">extended namespace</a>, <a href="../../../../index.html#info">info</a>, <a href="../../../../index.html#namespace_unknown">namespace unknown</a>, <a href="../../../../index.html#namespace_utilities">namespace utilities</a>, <a href="../../../../index.html#state_de_serialization">state (de)serialization</a>, <a href="../../../../index.html#unknown_hooking">unknown hooking</a>, <a href="../../../../index.html#utilities">utilities</a></p>
</div>
<div id="copyright" class="doctools_section"><h2><a name="copyright">Copyright</a></h2>
<p>Copyright &copy; 200? Neil Madden (http://wiki.tcl.tk/12790)<br>
Copyright &copy; 200? Various (http://wiki.tcl.tk/1489)<br>

be found in section <span class="sectref"><a href="#section5">OPTIONS</a></span>.</p></dd>
<dt><a name="8"><b class="cmd">::nameserv::configure</b></a></dt>
<dd><p>In this form the command returns a dictionary of all supported
options, and their current values. The list of supported options and
their meaning can be found in section <span class="sectref"><a href="#section5">OPTIONS</a></span>.</p></dd>
<dt><a name="9"><b class="cmd">::nameserv::configure</b> <b class="option">-option</b></a></dt>
<dd><p>In this form the command is an alias for
&quot;<b class="cmd">::nameserv::cget</b> <b class="option">-option</b>&quot;.
The list of supported options and their meaning can be found in
section <span class="sectref"><a href="#section5">OPTIONS</a></span>.</p></dd>
<dt><a name="10"><b class="cmd">::nameserv::configure</b> <b class="option">-option</b> <i class="arg">value</i>...</a></dt>
<dd><p>In this form the command is used to configure one or more of the
supported options. At least one option has to be specified, and each
option is followed by its new value.
The list of supported options and their meaning can be found in

be found in section <span class="sectref"><a href="#section3">OPTIONS</a></span>.</p></dd>
<dt><a name="5"><b class="cmd">::nameserv::server::configure</b></a></dt>
<dd><p>In this form the command returns a dictionary of all supported
options, and their current values. The list of supported options and
their meaning can be found in section <span class="sectref"><a href="#section3">OPTIONS</a></span>.</p></dd>
<dt><a name="6"><b class="cmd">::nameserv::server::configure</b> <b class="option">-option</b></a></dt>
<dd><p>In this form the command is an alias for
&quot;<b class="cmd">::nameserv::server::cget</b> <b class="option">-option</b>&quot;.
The list of supported options and their meaning can be found in
section <span class="sectref"><a href="#section3">OPTIONS</a></span>.</p></dd>
<dt><a name="7"><b class="cmd">::nameserv::server::configure</b> <b class="option">-option</b> <i class="arg">value</i>...</a></dt>
<dd><p>In this form the command is used to configure one or more of the
supported options. At least one option has to be specified, and each
option is followed by its new value.
The list of supported options and their meaning can be found in

<div class='fossil-doc' data-title='png - Image manipulation'>
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<div class="doctools">
<h1 class="doctools_title">png(n) 0.3 tcllib &quot;Image manipulation&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>png - PNG querying and manipulation of meta data</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">COMMANDS</a></li>
<li class="doctools_section"><a href="#section3">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.2</b></li>
<li>package require <b class="pkgname">crc32</b></li>
<li>package require <b class="pkgname">png <span class="opt">?0.3?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::png::validate</b> <i class="arg">file</i></a></li>
<li><a href="#2"><b class="cmd">::png::isPNG</b> <i class="arg">file</i></a></li>
<li><a href="#3"><b class="cmd">::png::imageInfo</b> <i class="arg">file</i></a></li>
<li><a href="#4"><b class="cmd">::png::getTimestamp</b> <i class="arg">file</i></a></li>
<li><a href="#5"><b class="cmd">::png::setTimestamp</b> <i class="arg">file</i> <i class="arg">time</i></a></li>
<li><a href="#6"><b class="cmd">::png::getComments</b> <i class="arg">file</i></a></li>
<li><a href="#7"><b class="cmd">::png::removeComments</b> <i class="arg">file</i></a></li>
<li><a href="#8"><b class="cmd">::png::addComment</b> <i class="arg">file</i> <i class="arg">keyword</i> <i class="arg">text</i></a></li>
<li><a href="#9"><b class="cmd">::png::addComment</b> <i class="arg">file</i> <i class="arg">keyword</i> <i class="arg">lang</i> <i class="arg">keyword2</i> <i class="arg">text</i></a></li>
<li><a href="#10"><b class="cmd">::png::getPixelDimension</b> <i class="arg">file</i></a></li>
<li><a href="#11"><b class="cmd">::png::image</b> <i class="arg">file</i></a></li>
<li><a href="#12"><b class="cmd">::png::write</b> <i class="arg">file</i> <i class="arg">data</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>This package provides commands to query and modify PNG images. PNG
stands for <i class="term">Portable Network Graphics</i> and is specified at
<a href="http://www.libpng.org/pub/png/spec/1.2">http://www.libpng.org/pub/png/spec/1.2</a>.</p>

<dt><a name="9"><b class="cmd">::png::addComment</b> <i class="arg">file</i> <i class="arg">keyword</i> <i class="arg">lang</i> <i class="arg">keyword2</i> <i class="arg">text</i></a></dt>
<dd><p>Adds a unicode (international) comment to the PNG image in <i class="arg">file</i>,
just before the first data chunk. Will throw an error if no data chunk
is found. <i class="arg">keyword</i> has to be less than 80 characters long to
conform to the PNG specification. <i class="arg">keyword2</i> is the translated
<i class="arg">keyword</i>, in the language specified by the language identifier
<i class="arg">lang</i>.</p></dd>
<dt><a name="10"><b class="cmd">::png::getPixelDimension</b> <i class="arg">file</i></a></dt>
<dd><p>Returns a dictionary with keys <b class="const">ppux</b>, <b class="const">ppuy</b> and
<b class="const">unit</b> if the information is present.  Otherwise, it returns the empty
string.</p>
<p>The values of <b class="const">ppux</b> and <b class="const">ppuy</b> return the pixel
per unit value in X or Y direction.</p>
<p>The allowed values for key <b class="const">unit</b> are <b class="const">meter</b> and
<b class="const">unknown</b>. In the case of meter, the dpi value can be calculated
by multiplying with the conversion factor <b class="const">0.0254</b>.</p></dd>
<dt><a name="11"><b class="cmd">::png::image</b> <i class="arg">file</i></a></dt>
<dd><p>Given a PNG file returns the image in the list of scanlines format used by Tk_GetColor.</p></dd>
<dt><a name="12"><b class="cmd">::png::write</b> <i class="arg">file</i> <i class="arg">data</i></a></dt>
<dd><p>Takes a list of scanlines in the Tk_GetColor format and writes the represented image
to <i class="arg">file</i>.</p></dd>
</dl>
</div>
<div id="section3" class="doctools_section"><h2><a name="section3">Bugs, Ideas, Feedback</a></h2>
<p>This document, and the package it describes, will undoubtedly contain
bugs and other problems.

<p>Here we describe the interface which has to be provided by the storage
callback so that pop3 servers following the interface of this module
are able to use it. The <i class="arg">mbox</i> argument is the storage reference
as returned by the <b class="method">lookup</b> method of the authentication
command, see section <span class="sectref"><a href="#section3">Authentication</a></span>.</p>
<dl class="doctools_definitions">
<dt><a name="14"><i class="arg">storageCmd</i> <b class="method">dele</b> <i class="arg">mbox</i> <i class="arg">msgList</i></a></dt>

<dd><p>Deletes the messages whose numeric ids are contained in the
<i class="arg">msgList</i> from the mailbox specified via <i class="arg">mbox</i>.</p></dd>
<dt><a name="15"><i class="arg">storageCmd</i> <b class="method">lock</b> <i class="arg">mbox</i></a></dt>
<dd><p>This method locks the specified mailbox for use by a single connection
to the server. This is necessary to prevent havoc if several
connections to the same mailbox are open. The complementary method is
<b class="method">unlock</b>. The command will return true if the lock could be set
successfully or false if not.</p></dd>

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 ] <hr>
<div class="doctools">
<h1 class="doctools_title">pt_peg_op(i) 1.1.0 tcllib &quot;Parser Tools&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>pt_peg_op - Parser Tools PE Grammar Utility Operations</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">API</a></li>
<li class="doctools_section"><a href="#section3">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.5</b></li>
<li>package require <b class="pkgname">pt::peg::op <span class="opt">?1.1.0?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::peg::peg::op</b> <b class="method">called</b> <i class="arg">container</i></a></li>
<li><a href="#2"><b class="cmd">::peg::peg::op</b> <b class="method">dechain</b> <i class="arg">container</i></a></li>
<li><a href="#3"><b class="cmd">::peg::peg::op</b> <b class="method">drop unreachable</b> <i class="arg">container</i></a></li>
<li><a href="#4"><b class="cmd">::peg::peg::op</b> <b class="method">drop unrealizable</b> <i class="arg">container</i></a></li>
<li><a href="#5"><b class="cmd">::peg::peg::op</b> <b class="method">flatten</b> <i class="arg">container</i></a></li>

<p>The content of any error message will not be passed back to the client.</p></dd>
<dt><b class="cmd">validate_recipient</b> callback</dt>
<dd><p>The validate_recipient callback is similar to the validate_sender
callback and permits you to verify a local mailbox and accept mail for
a local user address during RCPT command handling. To reject mail,
throw an error as above. The error message is ignored.</p></dd>
<dt><b class="cmd">deliverMIME</b> callback</dt>

<dd><p>The deliverMIME callback is called once a mail message has been
successfully passed to the server. A mime token is constructed from
the sender, recipients and data and the users procedure it called with
this single argument. When the call returns, the mime token is cleaned
up so if the user wishes to preserve the data she must make a copy.</p>
<pre class="doctools_example">
 proc deliverMIME {token} {
     set sender [lindex [mime::getheader $token From] 0]

listed in the <b class="method">options</b> procedure) but obviously does not check
the validity of the value passed to the <b class="method">set-<b class="option">option</b></b>
procedure, which should throw an error (for example by using the Tcl
error command) if the value is invalid.</p>
<p>The switched layer also keeps track of the options current
values, so that a <b class="method">set-<b class="option">option</b></b> procedure is called
only when the corresponding option value passed as parameter is
different from the current value (see <b class="variable">-option</b> data members
description).</p></dd>
<dt><b class="variable">-option</b></dt>
<dd><p>The <b class="variable">-option</b> data member is an options current value.
There is one for each option listed in the options procedure. It is a
read-only value which the switched layer checks against when an option
is changed.
It is rarely used at the layer derived from switched, except in the
few cases, such as in the following example:</p>
<pre class="doctools_example">
...

    puts "manufacturer: $switched::($this,-manufacturer)"
    ...
}
</pre>
<p>In this case, the manufacturer's name is stored at the switched
layer level (this is why the set-manufacturer procedure has nothing to
do) and later retrieved in the printData procedure.</p></dd>
<dt><b class="variable">complete</b></dt>
<dd><p>The <b class="variable">complete</b> data member (not to be confused with the
<b class="method">complete</b> procedure) is a boolean.
Its initial value is <b class="const">false</b> and it is set to <b class="const">true</b> at
the very end of the switched <b class="method">complete</b> procedure.
It becomes useful when some options should be set at construction time
only and not dynamically, as the following example shows:</p>
<pre class="doctools_example">
proc car::set-width {this value} {
    if {$switched::($this,complete)} {

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<h1 class="doctools_title">struct::disjointset(n) 1.1 tcllib &quot;Tcl Data Structures&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>struct::disjointset - Disjoint set data structure</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">API</a></li>
<li class="doctools_section"><a href="#section3">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.6</b></li>
<li>package require <b class="pkgname">struct::disjointset <span class="opt">?1.1?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::struct::disjointset</b> <i class="arg">disjointsetName</i></a></li>
<li><a href="#2"><i class="arg">disjointsetName</i> <i class="arg">option</i> <span class="opt">?<i class="arg">arg arg ...</i>?</span></a></li>
<li><a href="#3"><i class="arg">disjointsetName</i> <b class="method">add-element</b> <i class="arg">item</i></a></li>
<li><a href="#4"><i class="arg">disjointsetName</i> <b class="method">add-partition</b> <i class="arg">elements</i></a></li>
<li><a href="#5"><i class="arg">disjointsetName</i> <b class="method">partitions</b></a></li>
<li><a href="#6"><i class="arg">disjointsetName</i> <b class="method">num-partitions</b></a></li>
<li><a href="#7"><i class="arg">disjointsetName</i> <b class="method">equal</b> <i class="arg">a</i> <i class="arg">b</i></a></li>
<li><a href="#8"><i class="arg">disjointsetName</i> <b class="method">merge</b> <i class="arg">a</i> <i class="arg">b</i></a></li>
<li><a href="#9"><i class="arg">disjointsetName</i> <b class="method">find</b> <i class="arg">e</i></a></li>
<li><a href="#10"><i class="arg">disjointsetName</i> <b class="method">exemplars</b></a></li>
<li><a href="#11"><i class="arg">disjointsetName</i> <b class="method">find-exemplar</b> <i class="arg">e</i></a></li>
<li><a href="#12"><i class="arg">disjointsetName</i> <b class="method">destroy</b></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>This package provides <i class="term">disjoint sets</i>. An alternative name for
this kind of structure is <i class="term">merge-find</i>.</p>
<p>Normally when dealing with sets and their elements the question is &quot;Is

general form:</p>
<dl class="doctools_definitions">
<dt><a name="2"><i class="arg">disjointsetName</i> <i class="arg">option</i> <span class="opt">?<i class="arg">arg arg ...</i>?</span></a></dt>
<dd><p>The <b class="cmd">option</b> and the <i class="arg">arg</i>s determine the exact behavior of
the command. The following commands are possible for disjointset
objects:</p></dd>
</dl></dd>
<dt><a name="3"><i class="arg">disjointsetName</i> <b class="method">add-element</b> <i class="arg">item</i></a></dt>
<dd><p>Creates a new partition in the specified disjoint set, and fills it
with the single item <i class="arg">item</i>.  The command maintains
the integrity of the disjoint set, i.e. it verifies that none of the
<i class="arg">elements</i> are already part of the disjoint set and throws an
error otherwise.</p>
<p>The result of this method is the empty string.</p>
<p>This method runs in constant time.</p></dd>
<dt><a name="4"><i class="arg">disjointsetName</i> <b class="method">add-partition</b> <i class="arg">elements</i></a></dt>
<dd><p>Creates a new partition in specified disjoint set, and fills it with
the values found in the set of <i class="arg">elements</i>. The command maintains
the integrity of the disjoint set, i.e. it verifies that none of the
<i class="arg">elements</i> are already part of the disjoint set and throws an
error otherwise.</p>
<p>The result of the command is the empty string.</p>
<p>This method runs in time proportional to the size of <i class="arg">elements</i>].</p></dd>
<dt><a name="5"><i class="arg">disjointsetName</i> <b class="method">partitions</b></a></dt>
<dd><p>Returns the set of partitions the named disjoint set currently
consists of. The form of the result is a list of lists; the inner
lists contain the elements of the partitions.</p>
<p>This method runs in time O(N*alpha(N)),
where N is the number of elements in the disjoint set and alpha
is the inverse Ackermann function.</p></dd>
<dt><a name="6"><i class="arg">disjointsetName</i> <b class="method">num-partitions</b></a></dt>
<dd><p>Returns the number of partitions the named disjoint set currently
consists of.</p>
<p>This method runs in constant time.</p></dd>
<dt><a name="7"><i class="arg">disjointsetName</i> <b class="method">equal</b> <i class="arg">a</i> <i class="arg">b</i></a></dt>
<dd><p>Determines if the two elements <i class="arg">a</i> and <i class="arg">b</i> of the disjoint set
belong to the same partition. The result of the method is a boolean
value, <b class="const">True</b> if the two elements are contained in the same
partition, and <b class="const">False</b> otherwise.</p>
<p>An error will be thrown if either <i class="arg">a</i> or <i class="arg">b</i> are not elements
of the disjoint set.</p>
<p>This method runs in amortized time O(alpha(N)), where N is the number of
elements in the larger partition and alpha is the inverse Ackermann function.</p></dd>
<dt><a name="8"><i class="arg">disjointsetName</i> <b class="method">merge</b> <i class="arg">a</i> <i class="arg">b</i></a></dt>
<dd><p>Determines the partitions the elements <i class="arg">a</i> and <i class="arg">b</i> are
contained in and merges them into a single partition.  If the two
elements were already contained in the same partition nothing will
change.</p>
<p>The result of the method is the empty string.</p>
<p>This method runs in amortized time O(alpha(N)), where N is the number of
items in the larger of the partitions being merged. The worst case time
is O(N).</p></dd>
<dt><a name="9"><i class="arg">disjointsetName</i> <b class="method">find</b> <i class="arg">e</i></a></dt>
<dd><p>Returns a list of the members of the partition of the disjoint set
which contains the element
<i class="arg">e</i>.</p>
<p>This method runs in O(N*alpha(N)) time, where N is the total number of
items in the disjoint set and alpha is the inverse Ackermann function,
See <b class="method">find-exemplar</b> for a faster method, if all that is needed
is a unique identifier for the partition, rather than an enumeration
of all its elements.</p></dd>
<dt><a name="10"><i class="arg">disjointsetName</i> <b class="method">exemplars</b></a></dt>
<dd><p>Returns a list containing an exemplar of each partition in the disjoint
set. The exemplar is a member of the partition, chosen arbitrarily.</p>
<p>This method runs in O(N*alpha(N)) time, where N is the total number of items
in the disjoint set and alpha is the inverse Ackermann function.</p></dd>
<dt><a name="11"><i class="arg">disjointsetName</i> <b class="method">find-exemplar</b> <i class="arg">e</i></a></dt>
<dd><p>Returns the exemplar of the partition of the disjoint set containing
the element <i class="arg">e</i>.  Throws an error if <i class="arg">e</i> is not found in the
disjoint set.  The exemplar is an arbitrarily chosen member of the partition.
The only operation that will change the exemplar of any partition is
<b class="method">merge</b>.</p>
<p>This method runs in O(alpha(N)) time, where N is the number of items in
the partition containing E, and alpha is the inverse Ackermann function.</p></dd>
<dt><a name="12"><i class="arg">disjointsetName</i> <b class="method">destroy</b></a></dt>
<dd><p>Destroys the disjoint set object and all associated memory.</p></dd>
</dl>
</div>
<div id="section3" class="doctools_section"><h2><a name="section3">Bugs, Ideas, Feedback</a></h2>
<p>This document, and the package it describes, will undoubtedly contain
bugs and other problems.
Please report such in the category <em>struct :: disjointset</em> of the

<li class="doctools_section"><a href="#category">Category</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.6</b></li>
<li>package require <b class="pkgname">struct::graph::op <span class="opt">?0.11.3?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">struct::graph::op::toAdjacencyMatrix</b> <i class="arg">g</i></a></li>
<li><a href="#2"><b class="cmd">struct::graph::op::toAdjacencyList</b> <i class="arg">G</i> <span class="opt">?<i class="arg">options</i>...?</span></a></li>
<li><a href="#3"><b class="cmd">struct::graph::op::kruskal</b> <i class="arg">g</i></a></li>
<li><a href="#4"><b class="cmd">struct::graph::op::prim</b> <i class="arg">g</i></a></li>

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<h1 class="doctools_title">struct::list(n) 1.8.4 tcllib &quot;Tcl Data Structures&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>struct::list - Procedures for manipulating lists</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>

<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.4</b></li>
<li>package require <b class="pkgname">struct::list <span class="opt">?1.8.4?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::struct::list</b> <b class="method">longestCommonSubsequence</b> <i class="arg">sequence1</i> <i class="arg">sequence2</i> <span class="opt">?<i class="arg">maxOccurs</i>?</span></a></li>
<li><a href="#2"><b class="cmd">::struct::list</b> <b class="method">longestCommonSubsequence2</b> <i class="arg">sequence1 sequence2</i> <span class="opt">?<i class="arg">maxOccurs</i>?</span></a></li>
<li><a href="#3"><b class="cmd">::struct::list</b> <b class="method">lcsInvert</b> <i class="arg">lcsData</i> <i class="arg">len1</i> <i class="arg">len2</i></a></li>
<li><a href="#4"><b class="cmd">::struct::list</b> <b class="method">lcsInvert2</b> <i class="arg">lcs1</i> <i class="arg">lcs2</i> <i class="arg">len1</i> <i class="arg">len2</i></a></li>
<li><a href="#5"><b class="cmd">::struct::list</b> <b class="method">lcsInvertMerge</b> <i class="arg">lcsData</i> <i class="arg">len1</i> <i class="arg">len2</i></a></li>

<dd><p>Generates the part of the command line or the synopsis that is specific to an argument. The generated string has to indicate if an argument is optional, named and if it is a flag.</p>
<p>The following parameters are provided to this procedure:</p>
<dl class="doctools_definitions">
   
<dt><i class="arg">Name</i></dt>
<dd><p>Name of the argument</p></dd>
<dt><i class="arg">IsOptional</i></dt>
<dd><p>If true (=<b class="const">1</b>) the argument is optional which should be indicated by the generated string (for example by putting the argument into brackets {[]} or into question marks '?'):</p>
<pre class="doctools_example">gen(TXT,ArgumentString) mtype 1 0 string -&gt; <em>&quot;[mtype]&quot;</em></pre>
</dd>
<dt><i class="arg">IsNamed</i></dt>
<dd><p>If true (=<b class="const">1</b>) an argument is a named argument (option). The generated string should in this case contain the argument/option name, followed by the argument itself:</p>
<pre class="doctools_example">gen(TXT,ArgumentString) mtype 0 1 string -&gt; <em>&quot;-mtype &lt;mtype&gt;&quot;</em></pre>
<p>Named arguments can also be optional:</p>
<pre class="doctools_example">gen(TXT,ArgumentString) mtype 1 1 string -&gt; <em>&quot;[-mtype &lt;mtype&gt;]&quot;</em></pre>

<p>Named arguments can be defined multiple times. If the named argument has the <em>-multiply</em> attribute, all argument values will be collected in a list. Otherwise, only the last provided attribute value will be retained:</p>
<pre class="doctools_example">my_proc <b class="cmd">-n1 N1 -n2 N2 -n1 M1 U1 U2</b>
<em>-&gt; n1:'M1', n2:'N2', u1:'U1', u2:'U2'</em></pre>
<p>The name of the first unnamed argument has therefore not to start with the '-' character. The unnamed argument is otherwise considered as name of another named argument. This is especially important if the first unnamed argument is given by a variable that can contain any character strings:</p>
<pre class="doctools_example">my_proc <b class="cmd">-n1 N1 -n2 N2 &quot;-&gt;&quot; &quot;&lt;-&quot;</b>
<em>-&gt; my_proc: Argument '-&gt;' not known</em>
set U1 &quot;-&gt;&quot;
my_proc <b class="cmd">-n1 N1 -n2 N2 $U1 U2</b>
my_proc: Argument '-&gt;' not known</pre>
<p>The '--' flag allows separating unambiguously the unnamed arguments from the named arguments. All data after the '--' flag will be considered as unnamed argument:</p>
<pre class="doctools_example">my_proc <b class="cmd">-n1 N1 -n2 N2 -- &quot;-&gt;&quot; &quot;&lt;-&quot;</b>
<em>-&gt; n1:'N1', n2:'N2', u1:'-&gt;', u2:'&lt;-'</em>
set U1 &quot;-&gt;&quot;
my_proc <b class="cmd">-n1 N1 -n2 N2 -- $U1 U2</b>
<em>-&gt; n1:'N1', n2:'N2', u1:'-&gt;', u2:'&lt;-'</em></pre>

there are no space chars at the end of this line, and there may be
some space chars at the beginning, despite of the <b class="option">-full</b> option.</p></dd>
</dl></dd>
<dt><b class="option">-length</b> <i class="arg">integer</i></dt>
<dd><p>Set the length of the <em>logical</em> line in the string to
<i class="arg">integer</i>.  <i class="arg">integer</i> must be a positive integer
value. Defaults to <b class="const">72</b>.</p></dd>
<dt><b class="option">-strictlength</b> <i class="arg">boolean</i></dt>

<dd><p>If set to <b class="const">false</b> (default), a line can exceed the specified
<b class="option">-length</b> if a single word is longer than <b class="option">-length</b>. If
set to <b class="const">true</b>, words that are longer than <b class="option">-length</b> are
split so that no line exceeds the specified <b class="option">-length</b>.</p></dd>
</dl></dd>
<dt><a name="2"><b class="cmd">::textutil::adjust::readPatterns</b> <i class="arg">filename</i></a></dt>
<dd><p>Loads the internal storage for hyphenation patterns with the contents
of the file <i class="arg">filename</i>. This has to be done prior to calling

<dt><a name="3"><b class="cmd">::websocket::server</b> <i class="arg">sock</i></a></dt>
<dd><p>This command registers the (accept) socket <i class="arg">sock</i> as the
identifier fo an HTTP server that is capable of doing WebSockets.
Paths onto which this server will listen for incoming connections
should be declared using <b class="cmd">::websocket::live</b>.</p></dd>
<dt><a name="4"><b class="cmd">::websocket::live</b> <i class="arg">sock</i> <i class="arg">path</i> <i class="arg">cb</i> <span class="opt">?<i class="arg">proto</i>?</span></a></dt>
<dd><p>This procedure registers callbacks that will be performed on a
WebSocket compliant server registered with <b class="cmd">::websocket::server</b>
whenever a client connects to a matching path and protocol. 
<i class="arg">sock</i> is the listening socket of the websocket compliant server
declared using <b class="cmd">::websocket::server</b>.  <i class="arg">path</i> is a glob-style
path to match in client request, whenever this will occur.  <i class="arg">cb</i>
is the command to callback (see Callbacks).  <i class="arg">proto</i> is a
glob-style protocol name matcher.</p></dd>
<dt><a name="5"><b class="cmd">::websocket::test</b> <i class="arg">srvSock</i> <i class="arg">cliSock</i> <i class="arg">path</i> <span class="opt">?<i class="arg">hdrs</i>?</span> <span class="opt">?<i class="arg">qry</i>?</span></a></dt>

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<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='math_calculus'><a href="files/modules/math/calculus.html">math::calculus</a></td>
<td class="#doctools_tocright">Integration and ordinary differential equations</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='math_calculus_romberg'><a href="files/modules/math/romberg.html">math::calculus::romberg</a></td>
<td class="#doctools_tocright">Romberg integration</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='math_calculus_symdiff'><a href="files/modules/math/symdiff.html">math::calculus::symdiff</a></td>
<td class="#doctools_tocright">Symbolic differentiation for Tcl</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='math_combinatorics'><a href="files/modules/math/combinatorics.html">math::combinatorics</a></td>
<td class="#doctools_tocright">Combinatorial functions in the Tcl Math Library</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='math_complexnumbers'><a href="files/modules/math/qcomplex.html">math::complexnumbers</a></td>
<td class="#doctools_tocright">Straightforward complex number package</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='math_constants'><a href="files/modules/math/constants.html">math::constants</a></td>
<td class="#doctools_tocright">Mathematical and numerical constants</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='math_decimal'><a href="files/modules/math/decimal.html">math::decimal</a></td>
<td class="#doctools_tocright">General decimal arithmetic</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='math_exact'><a href="files/modules/math/exact.html">math::exact</a></td>
<td class="#doctools_tocright">Exact Real Arithmetic</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='math_fourier'><a href="files/modules/math/fourier.html">math::fourier</a></td>
<td class="#doctools_tocright">Discrete and fast fourier transforms</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='math_fuzzy'><a href="files/modules/math/fuzzy.html">math::fuzzy</a></td>
<td class="#doctools_tocright">Fuzzy comparison of floating-point numbers</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='math_geometry'><a href="files/modules/math/math_geometry.html">math::geometry</a></td>
<td class="#doctools_tocright">Geometrical computations</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='math_interpolate'><a href="files/modules/math/interpolate.html">math::interpolate</a></td>
<td class="#doctools_tocright">Interpolation routines</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='math_linearalgebra'><a href="files/modules/math/linalg.html">math::linearalgebra</a></td>
<td class="#doctools_tocright">Linear Algebra</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='math_numtheory'><a href="files/modules/math/numtheory.html">math::numtheory</a></td>
<td class="#doctools_tocright">Number Theory</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='math_optimize'><a href="files/modules/math/optimize.html">math::optimize</a></td>
<td class="#doctools_tocright">Optimisation routines</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='math_pca'><a href="files/modules/math/pca.html">math::PCA</a></td>
<td class="#doctools_tocright">Package for Principal Component Analysis</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='math_polynomials'><a href="files/modules/math/polynomials.html">math::polynomials</a></td>
<td class="#doctools_tocright">Polynomial functions</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='math_rationalfunctions'><a href="files/modules/math/rational_funcs.html">math::rationalfunctions</a></td>
<td class="#doctools_tocright">Polynomial functions</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='math_roman'><a href="files/modules/math/roman.html">math::roman</a></td>
<td class="#doctools_tocright">Tools for creating and manipulating roman numerals</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='math_special'><a href="files/modules/math/special.html">math::special</a></td>
<td class="#doctools_tocright">Special mathematical functions</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='math_statistics'><a href="files/modules/math/statistics.html">math::statistics</a></td>
<td class="#doctools_tocright">Basic statistical functions and procedures</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='math_trig'><a href="files/modules/math/trig.html">math::trig</a></td>
<td class="#doctools_tocright">Trigonometric anf hyperbolic functions</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='md4'><a href="files/modules/md4/md4.html">md4</a></td>
<td class="#doctools_tocright">MD4 Message-Digest Algorithm</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='md5'><a href="files/modules/md5/md5.html">md5</a></td>
<td class="#doctools_tocright">MD5 Message-Digest Algorithm</td>

<td class="#doctools_tocright">Special mathematical functions</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='math_statistics'><a href="tcllib/files/modules/math/statistics.html">math::statistics</a></td>
<td class="#doctools_tocright">Basic statistical functions and procedures</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='math_trig'><a href="tcllib/files/modules/math/trig.html">math::trig</a></td>
<td class="#doctools_tocright">Trigonometric anf hyperbolic functions</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='simulation_annealing'><a href="tcllib/files/modules/simulation/annealing.html">simulation::annealing</a></td>
<td class="#doctools_tocright">Simulated annealing</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='simulation_montecarlo'><a href="tcllib/files/modules/simulation/montecarlo.html">simulation::montecarlo</a></td>
<td class="#doctools_tocright">Monte Carlo simulations</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='simulation_random'><a href="tcllib/files/modules/simulation/simulation_random.html">simulation::random</a></td>
<td class="#doctools_tocright">Pseudo-random number generators</td>
</tr>
</table></dl>
<dl><dt><a name='networking'>Networking<dd>
<table class="#doctools_toc">
<tr class="#doctools_toceven" >

<td class="#doctools_tocright">Defered execution</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='lambda'><a href="tcllib/files/modules/lambda/lambda.html">lambda</a></td>
<td class="#doctools_tocright">Utility commands for anonymous procedures</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='lazyset'><a href="tcllib/files/modules/lazyset/lazyset.html">lazyset</a></td>
<td class="#doctools_tocright">Lazy evaluation</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='oo_util'><a href="tcllib/files/modules/ooutil/ooutil.html">oo::util</a></td>
<td class="#doctools_tocright">Utility commands for TclOO</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='oo_util'><a href="tcllib/files/modules/tool/meta.html">oo::util</a></td>
<td class="#doctools_tocright">Utility commands for TclOO</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='throw'><a href="tcllib/files/modules/try/tcllib_throw.html">throw</a></td>
<td class="#doctools_tocright">throw - Throw an error exception with a message</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='tool_dict_ensemble'><a href="tcllib/files/modules/tool/tool_dict_ensemble.html">tool::dict_ensemble</a></td>
<td class="#doctools_tocright">Dictionary Tools</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='try'><a href="tcllib/files/modules/try/tcllib_try.html">try</a></td>
<td class="#doctools_tocright">try - Trap and process errors and exceptions</td>
</tr>
</table></dl>
<dl><dt><a name='validation_type_checking'>Validation, Type checking<dd>
<table class="#doctools_toc">
<tr class="#doctools_toceven" >

</table></dl>
<dl><dt><a name='lambda'>lambda<dd>
<table class="#doctools_toc">
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='lambda'><a href="tcllib/files/modules/lambda/lambda.html">lambda</a></td>
<td class="#doctools_tocright">Utility commands for anonymous procedures</td>
</tr>
</table></dl>
<dl><dt><a name='lazyset'>lazyset<dd>
<table class="#doctools_toc">
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='lazyset'><a href="tcllib/files/modules/lazyset/lazyset.html">lazyset</a></td>
<td class="#doctools_tocright">Lazy evaluation</td>
</tr>
</table></dl>
<dl><dt><a name='ldap'>ldap<dd>
<table class="#doctools_toc">
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='ldap'><a href="tcllib/files/modules/ldap/ldap.html">ldap</a></td>
<td class="#doctools_tocright">LDAP client</td>
</tr>

<td class="#doctools_tocright">Special mathematical functions</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='math_statistics'><a href="tcllib/files/modules/math/statistics.html">math::statistics</a></td>
<td class="#doctools_tocright">Basic statistical functions and procedures</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='math_trig'><a href="tcllib/files/modules/math/trig.html">math::trig</a></td>
<td class="#doctools_tocright">Trigonometric anf hyperbolic functions</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='tclrep_machineparameters'><a href="tcllib/files/modules/math/machineparameters.html">tclrep/machineparameters</a></td>
<td class="#doctools_tocright">Compute double precision machine parameters.</td>
</tr>
</table></dl>
<dl><dt><a name='md4'>md4<dd>
<table class="#doctools_toc">
<tr class="#doctools_toceven" >

<td class="#doctools_tocright">Special mathematical functions</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='math_statistics'><a href="tcllib/files/modules/math/statistics.html">math::statistics</a></td>
<td class="#doctools_tocright">Basic statistical functions and procedures</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='math_trig'><a href="tcllib/files/modules/math/trig.html">math::trig</a></td>
<td class="#doctools_tocright">Trigonometric anf hyperbolic functions</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='simulation_annealing'><a href="tcllib/files/modules/simulation/annealing.html">simulation::annealing</a></td>
<td class="#doctools_tocright">Simulated annealing</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='simulation_montecarlo'><a href="tcllib/files/modules/simulation/montecarlo.html">simulation::montecarlo</a></td>
<td class="#doctools_tocright">Monte Carlo simulations</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='simulation_random'><a href="tcllib/files/modules/simulation/simulation_random.html">simulation::random</a></td>
<td class="#doctools_tocright">Pseudo-random number generators</td>
</tr>
</table></dl>
<dl><dt><a name='networking'>Networking<dd>
<table class="#doctools_toc">
<tr class="#doctools_toceven" >

<td class="#doctools_tocright">Defered execution</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='lambda'><a href="tcllib/files/modules/lambda/lambda.html">lambda</a></td>
<td class="#doctools_tocright">Utility commands for anonymous procedures</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='lazyset'><a href="tcllib/files/modules/lazyset/lazyset.html">lazyset</a></td>
<td class="#doctools_tocright">Lazy evaluation</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='oo_util'><a href="tcllib/files/modules/ooutil/ooutil.html">oo::util</a></td>
<td class="#doctools_tocright">Utility commands for TclOO</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='oo_util'><a href="tcllib/files/modules/tool/meta.html">oo::util</a></td>
<td class="#doctools_tocright">Utility commands for TclOO</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='throw'><a href="tcllib/files/modules/try/tcllib_throw.html">throw</a></td>
<td class="#doctools_tocright">throw - Throw an error exception with a message</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='tool_dict_ensemble'><a href="tcllib/files/modules/tool/tool_dict_ensemble.html">tool::dict_ensemble</a></td>
<td class="#doctools_tocright">Dictionary Tools</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='try'><a href="tcllib/files/modules/try/tcllib_try.html">try</a></td>
<td class="#doctools_tocright">try - Trap and process errors and exceptions</td>
</tr>
</table></dl>
<dl><dt><a name='validation_type_checking'>Validation, Type checking<dd>
<table class="#doctools_toc">
<tr class="#doctools_toceven" >

</table></dl>
<dl><dt><a name='lambda'>lambda<dd>
<table class="#doctools_toc">
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='lambda'><a href="tcllib/files/modules/lambda/lambda.html">lambda</a></td>
<td class="#doctools_tocright">Utility commands for anonymous procedures</td>
</tr>
</table></dl>
<dl><dt><a name='lazyset'>lazyset<dd>
<table class="#doctools_toc">
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='lazyset'><a href="tcllib/files/modules/lazyset/lazyset.html">lazyset</a></td>
<td class="#doctools_tocright">Lazy evaluation</td>
</tr>
</table></dl>
<dl><dt><a name='ldap'>ldap<dd>
<table class="#doctools_toc">
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='ldap'><a href="tcllib/files/modules/ldap/ldap.html">ldap</a></td>
<td class="#doctools_tocright">LDAP client</td>
</tr>

<td class="#doctools_tocright">Special mathematical functions</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='math_statistics'><a href="tcllib/files/modules/math/statistics.html">math::statistics</a></td>
<td class="#doctools_tocright">Basic statistical functions and procedures</td>
</tr>
<tr class="#doctools_toceven" >
<td class="#doctools_tocleft" ><a name='math_trig'><a href="tcllib/files/modules/math/trig.html">math::trig</a></td>
<td class="#doctools_tocright">Trigonometric anf hyperbolic functions</td>
</tr>
<tr class="#doctools_tocodd"  >
<td class="#doctools_tocleft" ><a name='tclrep_machineparameters'><a href="tcllib/files/modules/math/machineparameters.html">tclrep/machineparameters</a></td>
<td class="#doctools_tocright">Compute double precision machine parameters.</td>
</tr>
</table></dl>
<dl><dt><a name='md4'>md4<dd>
<table class="#doctools_toc">
<tr class="#doctools_toceven" >

'\"
'\" Generated from file 'async\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2008 Andreas Kupries <andreas_kupries@users\&.sourceforge\&.net>
'\"
.TH "cache::async" n 0\&.3\&.1 tcllib "In-memory caches"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

..
.BS
.SH NAME
cache::async \- Asynchronous in-memory cache
.SH SYNOPSIS
package require \fBTcl  8\&.4\fR
.sp
package require \fBcache::async  ?0\&.3\&.1?\fR
.sp
\fB::cache::async\fR \fIobjectName\fR \fIcommandprefix\fR ?\fIoptions\fR\&.\&.\&.?
.sp
\fIobjectName\fR \fBget\fR \fIkey\fR \fIdonecmdprefix\fR
.sp
\fIobjectName\fR \fBset\fR \fIkey\fR \fIvalue\fR
.sp

.sp
\fB::cron::task info\fR \fIprocess\fR
.sp
\fB::cron::task set\fR \fIprocess\fR \fIfield\fR \fIvalue\fR \fI?field\&.\&.\&.?\fR \fI?value\&.\&.\&.?\fR
.sp
\fB::cron::wake\fR \fI?who?\fR
.sp
\fB::cron::clock_step\fR \fImilliseconds\fR
.sp
\fB::cron::clock_delay\fR \fImilliseconds\fR
.sp
\fB::cron::clock_sleep\fR \fIseconds\fR \fI?offset?\fR
.sp
\fB::cron::clock_set\fR \fInewtime\fR
.sp
.BE
.SH DESCRIPTION

\fB::cron::task info\fR \fIprocess\fR
Returns a dict describing \fIprocess\fR\&. See \fB::cron::task set\fR for a description of the options\&.
.TP
\fB::cron::task set\fR \fIprocess\fR \fIfield\fR \fIvalue\fR \fI?field\&.\&.\&.?\fR \fI?value\&.\&.\&.?\fR
.sp
If \fIprocess\fR does not exist, it is created\&. Options Include:
.RS
.TP
\fBcommand\fR
If \fBcoroutine\fR is black, a global command which implements this process\&. If \fBcoroutine\fR is not
black, the command to invoke to create or recreate the coroutine\&.
.TP
\fBcoroutine\fR
The name of the coroutine (if any) which implements this process\&.
.TP
\fBfrequency\fR
If -1, this process is terminated after the next event\&. If 0 this process should be called during every
idle event\&. If positive, this process should generate events periodically\&. The frequency is an integer number
of milliseconds between events\&.
.TP
\fBobject\fR
The object associated with this process or coroutine\&.
.TP
\fBscheduled\fR
If non-zero, the absolute time from the epoch (in milliseconds) that this process will trigger an event\&.
If zero, and the \fBfrequency\fR is also zero, this process is called every idle loop\&.
.TP
\fBrunning\fR
A boolean flag\&. If true it indicates the process never returned or yielded during the event loop,
and will not be called again until it does so\&.
.RE
.TP
\fB::cron::wake\fR \fI?who?\fR
Wake up cron, and arrange for its event loop to be run during the next Idle cycle\&.
.CS


::cron::wake {I just did something important}

.CE
.PP
.PP
Several utility commands are provided that are used internally within cron and for
testing cron, but may or may not be useful in the general cases\&.
.TP
\fB::cron::clock_step\fR \fImilliseconds\fR
.sp
Return a clock time absolute to the epoch which falls on the next
border between one second and the next for the value of \fImilliseconds\fR
.TP
\fB::cron::clock_delay\fR \fImilliseconds\fR
.sp
Return a clock time absolute to the epoch which falls on the next
border between one second and the next \fImilliseconds\fR in the future\&.
.TP
\fB::cron::clock_sleep\fR \fIseconds\fR \fI?offset?\fR
.sp
Return a clock time absolute to the epoch which falls exactly \fIseconds\fR in
the future\&. If offset is given it may be positive or negative, and will shift
the final time to before or after the second would flip\&.
.TP
\fB::cron::clock_set\fR \fInewtime\fR
.sp
Sets the internal clock for cron\&. This command will advance the time in 100ms
increment, triggering events, until the internal time catches up with \fInewtime\fR\&.
.sp
\fInewtime\fR is expressed in absolute milliseconds since the beginning of the epoch\&.
.PP
.PP
.SH "BUGS, IDEAS, FEEDBACK"
This document, and the package it describes, will undoubtedly contain
bugs and other problems\&.
Please report such in the category \fIodie\fR of the
\fITcllib Trackers\fR [http://core\&.tcl\&.tk/tcllib/reportlist]\&.

order, separated by commas\&.
.sp
The values are lists of the files the entry is touching\&.
.RE
.sp
.TP
\fB::doctools::cvs::toChangeLog\fR \fIevar\fR \fIcvar\fR \fIfvar\fR

The three arguments for this command are the same as the last three
arguments of the command \fB::doctools::cvs::scanLog\fR\&. This command
however expects them to be filled with information about one or more
logs\&. It takes this information and converts it into a text in the
format of a ChangeLog as accepted and generated by \fBemacs\fR\&. The
constructed text is returned as the result of the command\&.
.PP

in the given order\&. Regular text is not allowed within the header\&.
.PP
Given the above a less minimal example of a document is
.CS


[manpage_begin NAME SECTION VERSION]










[\fBcopyright {YEAR AUTHOR}\fR]
[\fBtitledesc TITLE\fR]
[\fBmoddesc   MODULE_TITLE\fR]
[\fBrequire   PACKAGE VERSION\fR]
[\fBrequire   PACKAGE\fR]
[description]
[manpage_end]

.CE
Remember that the whitespace is optional\&. The document
.CS


    [manpage_begin NAME SECTION VERSION]










    [copyright {YEAR AUTHOR}][titledesc TITLE][moddesc MODULE_TITLE]
    [require PACKAGE VERSION][require PACKAGE][description]
    [vset CATEGORY doctools]
[include \&.\&./doctools2base/include/feedback\&.inc]
[manpage_end]

.CE
has the same meaning as the example before\&.
.PP
On the other hand, if \fIwhitespace\fR is present it consists not
only of any sequence of characters containing the space character,
horizontal and vertical tabs, carriage return, and newline, but it may
contain comment markup as well, in the form of the \fBcomment\fR
command\&.
.CS


[\fBcomment { \&.\&.\&. }\fR]
[manpage_begin NAME SECTION VERSION]










[copyright {YEAR AUTHOR}]
[titledesc TITLE]
[moddesc   MODULE_TITLE][\fBcomment { \&.\&.\&. }\fR]
[require   PACKAGE VERSION]
[require   PACKAGE]
[description]
[manpage_end]

is possible to write
.CS


[\fBinclude FILE\fR]
[\fBvset VAR VALUE\fR]
[manpage_begin NAME SECTION VERSION]










[description]
[manpage_end]

.CE
Even more important, these two commands are allowed anywhere where a
markup command is allowed, without regard for any other
structure\&. I\&.e\&. for example in the header as well\&.
.CS


[manpage_begin NAME SECTION VERSION]










[\fBinclude FILE\fR]
[\fBvset VAR VALUE\fR]
[description]
[manpage_end]

.CE
The only restriction \fBinclude\fR has to obey is that the contents of

the next\&. The first paragraph is automatically opened at the beginning
of the body, by \fBdescription\fR\&. In the same manner the last
paragraph automatically ends at \fBmanpage_end\fR\&.
.CS


[manpage_begin NAME SECTION VERSION]










[description]
 \&.\&.\&.
[\fBpara\fR]
 \&.\&.\&.
[\fBpara\fR]
 \&.\&.\&.
[manpage_end]

.PP
Empty sections are \fInot\fR ignored\&. We are free to (not) use
paragraphs within sections\&.
.CS


[manpage_begin NAME SECTION VERSION]










[description]
 \&.\&.\&.
[\fBsection {Section A}\fR]
 \&.\&.\&.
[para]
 \&.\&.\&.
[\fBsection {Section B}\fR]

.PP
Empty subsections are \fInot\fR ignored\&. We are free to (not) use
paragraphs within subsections\&.
.CS


[manpage_begin NAME SECTION VERSION]










[description]
 \&.\&.\&.
[section {Section A}]
 \&.\&.\&.
[\fBsubsection {Sub 1}\fR]
 \&.\&.\&.
[para]

highlighting added\&.
It shows their use within a block of text, as the arguments of a list
item command (\fBcall\fR), and our ability to nest them\&.
.CS


  \&.\&.\&.
  [call [\fBcmd arg_def\fR] [\fBarg type\fR] [\fBarg name\fR] [\fBopt\fR [\fBarg mode\fR]]]

  Text structure\&. List element\&. Argument list\&. Automatically closes the
  previous list element\&. Specifies the data-[\fBarg type\fR] of the described
  argument of a command, its [\fBarg name\fR] and its i/o-[\fBarg mode\fR]\&. The
  latter is optional\&.
  \&.\&.\&.

The name of the variable where to store any incomplete HTML into\&. This
makes most sense for the incremental mode\&. The parser will throw an
error if it sees incomplete HTML and has no place to store it to\&. This
makes sense for the normal mode\&. Only incomplete tags are detected,
not missing tags\&.  Optional, defaults to 'no variable'\&.
.RE
.RS

.TP
\fIInterface to the command prefix\fR
In normal mode the parser will invoke the command prefix with four
arguments appended\&. See \fB::htmlparse::debugCallback\fR for a
description\&.
.sp
In incremental mode, however, the generated scripts will invoke the

'\"
'\" Generated from file 'lazyset\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2018 Roy Keene
'\"
.TH "lazyset" n 1 tcllib "Lazy evaluation for variables and arrays"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,
.\"	and indent is equivalent to second arg of .IP (shouldn't ever be
.\"	needed;  use .AS below instead)
.\"
.\" .AS ?type? ?name?
.\"	Give maximum sizes of arguments for setting tab stops.  Type and
.\"	name are examples of largest possible arguments that will be passed
.\"	to .AP later.  If args are omitted, default tab stops are used.
.\"
.\" .BS
.\"	Start box enclosure.  From here until next .BE, everything will be
.\"	enclosed in one large box.
.\"
.\" .BE
.\"	End of box enclosure.
.\"
.\" .CS
.\"	Begin code excerpt.
.\"
.\" .CE
.\"	End code excerpt.
.\"
.\" .VS ?version? ?br?
.\"	Begin vertical sidebar, for use in marking newly-changed parts
.\"	of man pages.  The first argument is ignored and used for recording
.\"	the version when the .VS was added, so that the sidebars can be
.\"	found and removed when they reach a certain age.  If another argument
.\"	is present, then a line break is forced before starting the sidebar.
.\"
.\" .VE
.\"	End of vertical sidebar.
.\"
.\" .DS
.\"	Begin an indented unfilled display.
.\"
.\" .DE
.\"	End of indented unfilled display.
.\"
.\" .SO ?manpage?
.\"	Start of list of standard options for a Tk widget. The manpage
.\"	argument defines where to look up the standard options; if
.\"	omitted, defaults to "options". The options follow on successive
.\"	lines, in three columns separated by tabs.
.\"
.\" .SE
.\"	End of list of standard options for a Tk widget.
.\"
.\" .OP cmdName dbName dbClass
.\"	Start of description of a specific option.  cmdName gives the
.\"	option's name as specified in the class command, dbName gives
.\"	the option's name in the option database, and dbClass gives
.\"	the option's class in the option database.
.\"
.\" .UL arg1 arg2
.\"	Print arg1 underlined, then print arg2 normally.
.\"
.\" .QW arg1 ?arg2?
.\"	Print arg1 in quotes, then arg2 normally (for trailing punctuation).
.\"
.\" .PQ arg1 ?arg2?
.\"	Print an open parenthesis, arg1 in quotes, then arg2 normally
.\"	(for trailing punctuation) and then a closing parenthesis.
.\"
.\"	# Set up traps and other miscellaneous stuff for Tcl/Tk man pages.
.if t .wh -1.3i ^B
.nr ^l \n(.l
.ad b
.\"	# Start an argument description
.de AP
.ie !"\\$4"" .TP \\$4
.el \{\
.   ie !"\\$2"" .TP \\n()Cu
.   el          .TP 15
.\}
.ta \\n()Au \\n()Bu
.ie !"\\$3"" \{\
\&\\$1 \\fI\\$2\\fP (\\$3)
.\".b
.\}
.el \{\
.br
.ie !"\\$2"" \{\
\&\\$1	\\fI\\$2\\fP
.\}
.el \{\
\&\\fI\\$1\\fP
.\}
.\}
..
.\"	# define tabbing values for .AP
.de AS
.nr )A 10n
.if !"\\$1"" .nr )A \\w'\\$1'u+3n
.nr )B \\n()Au+15n
.\"
.if !"\\$2"" .nr )B \\w'\\$2'u+\\n()Au+3n
.nr )C \\n()Bu+\\w'(in/out)'u+2n
..
.AS Tcl_Interp Tcl_CreateInterp in/out
.\"	# BS - start boxed text
.\"	# ^y = starting y location
.\"	# ^b = 1
.de BS
.br
.mk ^y
.nr ^b 1u
.if n .nf
.if n .ti 0
.if n \l'\\n(.lu\(ul'
.if n .fi
..
.\"	# BE - end boxed text (draw box now)
.de BE
.nf
.ti 0
.mk ^t
.ie n \l'\\n(^lu\(ul'
.el \{\
.\"	Draw four-sided box normally, but don't draw top of
.\"	box if the box started on an earlier page.
.ie !\\n(^b-1 \{\
\h'-1.5n'\L'|\\n(^yu-1v'\l'\\n(^lu+3n\(ul'\L'\\n(^tu+1v-\\n(^yu'\l'|0u-1.5n\(ul'
.\}
.el \}\
\h'-1.5n'\L'|\\n(^yu-1v'\h'\\n(^lu+3n'\L'\\n(^tu+1v-\\n(^yu'\l'|0u-1.5n\(ul'
.\}
.\}
.fi
.br
.nr ^b 0
..
.\"	# VS - start vertical sidebar
.\"	# ^Y = starting y location
.\"	# ^v = 1 (for troff;  for nroff this doesn't matter)
.de VS
.if !"\\$2"" .br
.mk ^Y
.ie n 'mc \s12\(br\s0
.el .nr ^v 1u
..
.\"	# VE - end of vertical sidebar
.de VE
.ie n 'mc
.el \{\
.ev 2
.nf
.ti 0
.mk ^t
\h'|\\n(^lu+3n'\L'|\\n(^Yu-1v\(bv'\v'\\n(^tu+1v-\\n(^Yu'\h'-|\\n(^lu+3n'
.sp -1
.fi
.ev
.\}
.nr ^v 0
..
.\"	# Special macro to handle page bottom:  finish off current
.\"	# box/sidebar if in box/sidebar mode, then invoked standard
.\"	# page bottom macro.
.de ^B
.ev 2
'ti 0
'nf
.mk ^t
.if \\n(^b \{\
.\"	Draw three-sided box if this is the box's first page,
.\"	draw two sides but no top otherwise.
.ie !\\n(^b-1 \h'-1.5n'\L'|\\n(^yu-1v'\l'\\n(^lu+3n\(ul'\L'\\n(^tu+1v-\\n(^yu'\h'|0u'\c
.el \h'-1.5n'\L'|\\n(^yu-1v'\h'\\n(^lu+3n'\L'\\n(^tu+1v-\\n(^yu'\h'|0u'\c
.\}
.if \\n(^v \{\
.nr ^x \\n(^tu+1v-\\n(^Yu
\kx\h'-\\nxu'\h'|\\n(^lu+3n'\ky\L'-\\n(^xu'\v'\\n(^xu'\h'|0u'\c
.\}
.bp
'fi
.ev
.if \\n(^b \{\
.mk ^y
.nr ^b 2
.\}
.if \\n(^v \{\
.mk ^Y
.\}
..
.\"	# DS - begin display
.de DS
.RS
.nf
.sp
..
.\"	# DE - end display
.de DE
.fi
.RE
.sp
..
.\"	# SO - start of list of standard options
.de SO
'ie '\\$1'' .ds So \\fBoptions\\fR
'el .ds So \\fB\\$1\\fR
.SH "STANDARD OPTIONS"
.LP
.nf
.ta 5.5c 11c
.ft B
..
.\"	# SE - end of list of standard options
.de SE
.fi
.ft R
.LP
See the \\*(So manual entry for details on the standard options.
..
.\"	# OP - start of full description for a single option
.de OP
.LP
.nf
.ta 4c
Command-Line Name:	\\fB\\$1\\fR
Database Name:	\\fB\\$2\\fR
Database Class:	\\fB\\$3\\fR
.fi
.IP
..
.\"	# CS - begin code excerpt
.de CS
.RS
.nf
.ta .25i .5i .75i 1i
..
.\"	# CE - end code excerpt
.de CE
.fi
.RE
..
.\"	# UL - underline word
.de UL
\\$1\l'|0\(ul'\\$2
..
.\"	# QW - apply quotation marks to word
.de QW
.ie '\\*(lq'"' ``\\$1''\\$2
.\"" fix emacs highlighting
.el \\*(lq\\$1\\*(rq\\$2
..
.\"	# PQ - apply parens and quotation marks to word
.de PQ
.ie '\\*(lq'"' (``\\$1''\\$2)\\$3
.\"" fix emacs highlighting
.el (\\*(lq\\$1\\*(rq\\$2)\\$3
..
.\"	# QR - quoted range
.de QR
.ie '\\*(lq'"' ``\\$1''\\-``\\$2''\\$3
.\"" fix emacs highlighting
.el \\*(lq\\$1\\*(rq\\-\\*(lq\\$2\\*(rq\\$3
..
.\"	# MT - "empty" string
.de MT
.QW ""
..
.BS
.SH NAME
lazyset \- Lazy evaluation
.SH SYNOPSIS
package require \fBTcl  8\&.5\fR
.sp
package require \fBlazyset  ?1?\fR
.sp
\fB::lazyset::variable\fR ?\fI-array boolean\fR? ?\fI-appendArgs boolean\fR? \fIvariableName\fR \fIcommandPrefix\fR
.sp
.BE
.SH DESCRIPTION
.PP
The \fBlazyset\fR package provides a mechanism for deferring execution
of code until a specific variable or any index of an array is referenced\&.
.SH COMMANDS
.TP
\fB::lazyset::variable\fR ?\fI-array boolean\fR? ?\fI-appendArgs boolean\fR? \fIvariableName\fR \fIcommandPrefix\fR
Arrange for the code specified as \fIcommandPrefix\fR to be executed when
the variable whose name is specified by \fIvariableName\fR is read for
the first time\&.
If the optional argument \fI-array boolean\fR is specified as true,
then the variable specified as \fIvariableName\fR is treated as an
array and attempting to read any index of the array causes that
index to be set by the \fIcommandPrefix\fR as they are read\&.
If the optional argument \fI-appendArgs boolean\fR is specified as
false, then the variable name and subnames are not appended to the
\fIcommandPrefix\fR before it is evaluated\&.  If the argument
\fI-appendArgs boolean\fR is not specified or is specified as true
then 1 or 2 additional arguments are appended to the \fIcommandPrefix\fR\&.
If \fI-array boolean\fR is specified as true, then 2 arguments are
appended corresponding to the name of the variable and the index,
otherwise 1 argument is appended containing the name of variable\&.
The \fIcommandPrefix\fR code is run in the same scope as the variable
is read\&.
.PP
.SH EXAMPLES
.CS


	::lazyset::variable page {apply {{name} {
		package require http
		set token [http::geturl http://www\&.tcl\&.tk/]
		set data [http::data $token]
		return $data
	}}}

	puts $page

.CE
.CS


	::lazyset::variable -array true page {apply {{name index} {
		package require http
		set token [http::geturl $index]
		set data [http::data $token]
		return $data
	}}}

	puts $page(http://www\&.tcl\&.tk/)

.CE
.CS


	::lazyset::variable -appendArgs false simple {
		return -level 0 42
	}

	puts $simple

.CE
.SH AUTHORS
Roy Keene
.SH "BUGS, IDEAS, FEEDBACK"
This document, and the package it describes, will undoubtedly contain
bugs and other problems\&.
Please report such in the category \fIutility\fR of the
\fITcllib Trackers\fR [http://core\&.tcl\&.tk/tcllib/reportlist]\&.
Please also report any ideas for enhancements you may have for either
package and/or documentation\&.
.PP
When proposing code changes, please provide \fIunified diffs\fR,
i\&.e the output of \fBdiff -u\fR\&.
.PP
Note further that \fIattachments\fR are strongly preferred over
inlined patches\&. Attachments can be made by going to the \fBEdit\fR
form of the ticket immediately after its creation, and then using the
left-most button in the secondary navigation bar\&.
.SH CATEGORY
Utility
.SH COPYRIGHT
.nf
Copyright (c) 2018 Roy Keene

.fi

their priority\&. This command can be used by the -command option of
lsort\&. The result is one of -1, 0 or 1 or an error\&. A result of -1
signals that level1 is of less priority than level2\&. 0 signals that
both levels have the same priority\&. 1 signals that level1 has higher
priority than level2\&.
.TP
\fB::log::lvSuppress\fR \fIlevel\fR {\fIsuppress\fR 1}

(Un)suppresses the output of messages having the specified
level\&. Unique abbreviations for the level are allowed here too\&.
.TP
\fB::log::lvSuppressLE\fR \fIlevel\fR {\fIsuppress\fR 1}

(Un)suppresses the output of messages having the specified level or
one of lesser priority\&. Unique abbreviations for the level are allowed
here too\&.
.TP
\fB::log::lvIsSuppressed\fR \fIlevel\fR
Asks the package whether the specified level is currently
suppressed\&. Unique abbreviations of level names are allowed\&.

\fIpolygon\fR - like a polyline, but the implicit assumption is that
the polyline is closed (if the first and last points do not coincide,
the missing segment is automatically added)\&.
.IP \(bu
\fIpoint set\fR - again a list of an even number of coordinates, but
the points are regarded without any ordering\&.
.IP \(bu
\fIcircle\fR - a list of three numbers, the first two are the coordinates of the
centre and the third is the radius\&.
.PP
.SH PROCEDURES
The package defines the following public procedures:
.TP
\fB::math::geometry::+\fR \fIpoint1\fR \fIpoint2\fR
Compute the sum of the two vectors given as points and return it\&.

list \fIcircle\fR
Circle that may or may not be intersected
.RE
.TP
\fB::math::geometry::intersectionCircleWithCircle\fR \fIcircle1\fR \fIcircle2\fR
Determine the points at which the given two circles intersect\&. There can
be zero, one or two points\&. (If the two circles touch the circle or are very close,
then one point is returned\&. An arbitrary margin of 1\&.0e-10 times the mean of the radii of
the two circles is used to determine this situation\&.)
.RS
.TP
list \fIcircle1\fR
First circle
.TP
list \fIcircle2\fR
Second circle

'\"
'\" Generated from file 'numtheory\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2010 Lars Hellström <Lars dot Hellstrom at residenset dot net>
'\"
.TH "math::numtheory" n 1\&.1\&.1 tcllib "Tcl Math Library"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

..
.BS
.SH NAME
math::numtheory \- Number Theory
.SH SYNOPSIS
package require \fBTcl  ?8\&.5?\fR
.sp
package require \fBmath::numtheory  ?1\&.1\&.1?\fR
.sp
\fBmath::numtheory::isprime\fR \fIN\fR ?\fIoption\fR \fIvalue\fR \&.\&.\&.?
.sp
\fBmath::numtheory::firstNprimes\fR \fIN\fR
.sp
\fBmath::numtheory::primesLowerThan\fR \fIN\fR
.sp
\fBmath::numtheory::primeFactors\fR \fIN\fR
.sp
\fBmath::numtheory::primesLowerThan\fR \fIN\fR
.sp
\fBmath::numtheory::primeFactors\fR \fIN\fR
.sp
\fBmath::numtheory::uniquePrimeFactors\fR \fIN\fR
.sp

\fBmath::numtheory::firstNprimes\fR \fIN\fR
Return the first N primes
.RS
.TP
integer \fIN\fR (in)
Number of primes to return
.RE
.TP
\fBmath::numtheory::primesLowerThan\fR \fIN\fR
Return the prime numbers lower/equal to N
.RS
.TP
integer \fIN\fR (in)
Maximum number to consider
.RE
.TP
\fBmath::numtheory::primeFactors\fR \fIN\fR
Return a list of the prime numbers in the number N
.RS
.TP
integer \fIN\fR (in)
Number to be factorised
.RE
.TP
\fBmath::numtheory::primesLowerThan\fR \fIN\fR
Return the prime numbers lower/equal to N
.RS
.TP
integer \fIN\fR (in)
Maximum number to consider

.de MT
.QW ""
..
.BS
.SH NAME
math::statistics \- Basic statistical functions and procedures
.SH SYNOPSIS
package require \fBTcl  8\&.5\fR
.sp
package require \fBmath::statistics  1\fR
.sp
\fB::math::statistics::mean\fR \fIdata\fR
.sp
\fB::math::statistics::min\fR \fIdata\fR
.sp

\fB::math::statistics::spearman-rank\fR \fIsample_a\fR \fIsample_b\fR
.sp
\fB::math::statistics::spearman-rank-extended\fR \fIsample_a\fR \fIsample_b\fR
.sp
\fB::math::statistics::kernel-density\fR \fIdata\fR opt \fI-option value\fR \&.\&.\&.
.sp
\fB::math::statistics::bootstrap\fR \fIdata\fR \fIsampleSize\fR ?numberSamples?
.sp
\fB::math::statistics::wasserstein-distance\fR \fIprob1\fR \fIprob2\fR
.sp
\fB::math::statistics::kl-divergence\fR \fIprob1\fR \fIprob2\fR
.sp
\fB::math::statistics::logistic-model\fR \fIxdata\fR \fIydata\fR
.sp
\fB::math::statistics::logistic-probability\fR \fIcoeffs\fR \fIx\fR
.sp
\fB::math::statistics::tstat\fR \fIdof\fR ?alpha?
.sp
\fB::math::statistics::mv-wls\fR \fIwt1\fR \fIweights_and_values\fR
.sp
\fB::math::statistics::mv-ols\fR \fIvalues\fR
.sp

- One or more groups of data to be checked
.RE
.sp
.TP
\fB::math::statistics::quantiles\fR \fIdata\fR \fIconfidence\fR
Return the quantiles for a given set of data
.RS

.TP
list \fIdata\fR
- List of raw data values
.sp
.TP
float \fIconfidence\fR
- Confidence level (0\&.95 or 0\&.99 for instance) or a list of confidence levels\&.

.TP
int \fIsampleSize\fR
Number of values per sample
.TP
int \fInumberSamples\fR
Number of samples (default: 1)
.RE
.TP
\fB::math::statistics::wasserstein-distance\fR \fIprob1\fR \fIprob2\fR
Compute the Wasserstein distance or earth mover's distance for two equidstantly spaced histograms
or probability densities\&. The histograms need not to be normalised to sum to one,
but they must have the same number of entries\&.
.sp
Note: the histograms are assumed to be based on the same equidistant intervals\&.
As the bounds are not passed, the value is expressed in the length of the intervals\&.
.RS
.TP
list \fIprob1\fR
List of values for the first histogram/probability density
.TP
list \fIprob2\fR
List of values for the second histogram/probability density
.RE
.TP
\fB::math::statistics::kl-divergence\fR \fIprob1\fR \fIprob2\fR
Compute the Kullback-Leibler (KL) divergence for two equidstantly spaced histograms
or probability densities\&. The histograms need not to be normalised to sum to one,
but they must have the same number of entries\&.
.sp
Note: the histograms are assumed to be based on the same equidistant intervals\&.
As the bounds are not passed, the value is expressed in the length of the intervals\&.
.sp
Note also that the KL divergence is not symmetric and that the second histogram
should not contain zeroes in places where the first histogram has non-zero values\&.
.RS
.TP
list \fIprob1\fR
List of values for the first histogram/probability density
.TP
list \fIprob2\fR
List of values for the second histogram/probability density
.RE
.TP
\fB::math::statistics::logistic-model\fR \fIxdata\fR \fIydata\fR
Estimate the coefficients of the logistic model that fits the data best\&. The data consist
of independent x-values and the outcome 0 or 1 for each of the x-values\&. The result
can be used to estimate the probability that a certain x-value gives 1\&.
.RS
.TP
list \fIxdata\fR
List of values for which the success (1) or failure (0) is known
.TP
list \fIydata\fR
List of successes or failures corresponding to each value in \fIxdata\fR\&.
.RE
.TP
\fB::math::statistics::logistic-probability\fR \fIcoeffs\fR \fIx\fR
Calculate the probability of success for the value \fIx\fR given the coefficients of the
logistic model\&.
.RS
.TP
list \fIcoeffs\fR
List of coefficients as determine by the \fBlogistic-model\fR command
.TP
float \fIx\fR
X-value for which the probability needs to be determined
.RE
.PP
.SH "MULTIVARIATE LINEAR REGRESSION"
Besides the linear regression with a single independent variable, the
statistics package provides two procedures for doing ordinary
least squares (OLS) and weighted least squares (WLS) linear regression
with several variables\&. They were written by Eric Kemp-Benedict\&.
.PP

'\"
'\" Generated from file 'trig\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2018 Arjen Markus
'\"
.TH "math::trig" n 1\&.0\&.0 tcllib "Tcl Math Library"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,
.\"	and indent is equivalent to second arg of .IP (shouldn't ever be
.\"	needed;  use .AS below instead)
.\"
.\" .AS ?type? ?name?
.\"	Give maximum sizes of arguments for setting tab stops.  Type and
.\"	name are examples of largest possible arguments that will be passed
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.\"	omitted, defaults to "options". The options follow on successive
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.\"	End of list of standard options for a Tk widget.
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.\"	(for trailing punctuation) and then a closing parenthesis.
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.if t .wh -1.3i ^B
.nr ^l \n(.l
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.de AP
.ie !"\\$4"" .TP \\$4
.el \{\
.   ie !"\\$2"" .TP \\n()Cu
.   el          .TP 15
.\}
.ta \\n()Au \\n()Bu
.ie !"\\$3"" \{\
\&\\$1 \\fI\\$2\\fP (\\$3)
.\".b
.\}
.el \{\
.br
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.\}
.el \{\
\&\\fI\\$1\\fP
.\}
.\}
..
.\"	# define tabbing values for .AP
.de AS
.nr )A 10n
.if !"\\$1"" .nr )A \\w'\\$1'u+3n
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.\"
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.nr )C \\n()Bu+\\w'(in/out)'u+2n
..
.AS Tcl_Interp Tcl_CreateInterp in/out
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.if n .fi
..
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.de BE
.nf
.ti 0
.mk ^t
.ie n \l'\\n(^lu\(ul'
.el \{\
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.\"	box if the box started on an earlier page.
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\h'-1.5n'\L'|\\n(^yu-1v'\l'\\n(^lu+3n\(ul'\L'\\n(^tu+1v-\\n(^yu'\l'|0u-1.5n\(ul'
.\}
.el \}\
\h'-1.5n'\L'|\\n(^yu-1v'\h'\\n(^lu+3n'\L'\\n(^tu+1v-\\n(^yu'\l'|0u-1.5n\(ul'
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.nr ^x \\n(^tu+1v-\\n(^Yu
\kx\h'-\\nxu'\h'|\\n(^lu+3n'\ky\L'-\\n(^xu'\v'\\n(^xu'\h'|0u'\c
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..
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'ie '\\$1'' .ds So \\fBoptions\\fR
'el .ds So \\fB\\$1\\fR
.SH "STANDARD OPTIONS"
.LP
.nf
.ta 5.5c 11c
.ft B
..
.\"	# SE - end of list of standard options
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.fi
.ft R
.LP
See the \\*(So manual entry for details on the standard options.
..
.\"	# OP - start of full description for a single option
.de OP
.LP
.nf
.ta 4c
Command-Line Name:	\\fB\\$1\\fR
Database Name:	\\fB\\$2\\fR
Database Class:	\\fB\\$3\\fR
.fi
.IP
..
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.BS
.SH NAME
math::trig \- Trigonometric anf hyperbolic functions
.SH SYNOPSIS
package require \fBTcl  8\&.5\fR
.sp
package require \fBmath::trig  1\&.0\&.0\fR
.sp
\fB::math::trig::radian_reduced\fR \fIangle\fR
.sp
\fB::math::trig::degree_reduced\fR \fIangle\fR
.sp
\fB::math::trig::cosec\fR \fIangle\fR
.sp
\fB::math::trig::sec\fR \fIangle\fR
.sp
\fB::math::trig::cotan\fR \fIangle\fR
.sp
\fB::math::trig::acosec\fR \fIvalue\fR
.sp
\fB::math::trig::asec\fR \fIvalue\fR
.sp
\fB::math::trig::acotan\fR \fIvalue\fR
.sp
\fB::math::trig::cosech\fR \fIvalue\fR
.sp
\fB::math::trig::sech\fR \fIvalue\fR
.sp
\fB::math::trig::cotanh\fR \fIvalue\fR
.sp
\fB::math::trig::asinh\fR \fIvalue\fR
.sp
\fB::math::trig::acosh\fR \fIvalue\fR
.sp
\fB::math::trig::atanh\fR \fIvalue\fR
.sp
\fB::math::trig::acosech\fR \fIvalue\fR
.sp
\fB::math::trig::asech\fR \fIvalue\fR
.sp
\fB::math::trig::acotanh\fR \fIvalue\fR
.sp
\fB::math::trig::sind\fR \fIangle\fR
.sp
\fB::math::trig::cosd\fR \fIangle\fR
.sp
\fB::math::trig::tand\fR \fIangle\fR
.sp
\fB::math::trig::cosecd\fR \fIangle\fR
.sp
\fB::math::trig::secd\fR \fIangle\fR
.sp
\fB::math::trig::cotand\fR \fIangle\fR
.sp
.BE
.SH DESCRIPTION
.PP
The \fImath::trig\fR package defines a set of trigonomic and hyperbolic functions
and their inverses\&. In addition it defines versions of the trigonomic functions
that take arguments in degrees instead of radians\&.
.PP
For easy use these functions may be imported into the \fItcl::mathfunc\fR namespace,
so that they can be used directly in the \fIexpr\fR command\&.
.SH FUNCTIONS
The functions \fIradian_reduced\fR and \fIdegree_reduced\fR return a reduced angle, in
respectively radians and degrees, in the intervals [0, 2pi) and [0, 360):
.TP
\fB::math::trig::radian_reduced\fR \fIangle\fR
Return the equivalent angle in the interval [0, 2pi)\&.
.RS
.TP
float \fIangle\fR
Angle (in radians)
.RE
.TP
\fB::math::trig::degree_reduced\fR \fIangle\fR
Return the equivalent angle in the interval [0, 360)\&.
.RS
.TP
float \fIangle\fR
Angle (in degrees)
.RE
.PP
The following trigonomic functions are defined in addition to the ones defined
in the \fIexpr\fR command:
.TP
\fB::math::trig::cosec\fR \fIangle\fR
Calculate the cosecant of the angle (1/cos(angle))
.RS
.TP
float \fIangle\fR
Angle (in radians)
.RE
.TP
\fB::math::trig::sec\fR \fIangle\fR
Calculate the secant of the angle (1/sin(angle))
.RS
.TP
float \fIangle\fR
Angle (in radians)
.RE
.TP
\fB::math::trig::cotan\fR \fIangle\fR
Calculate the cotangent of the angle (1/tan(angle))
.RS
.TP
float \fIangle\fR
Angle (in radians)
.RE
.PP
For these functions also the inverses are defined:
.TP
\fB::math::trig::acosec\fR \fIvalue\fR
Calculate the arc cosecant of the value
.RS
.TP
float \fIvalue\fR
Value of the argument
.RE
.TP
\fB::math::trig::asec\fR \fIvalue\fR
Calculate the arc secant of the value
.RS
.TP
float \fIvalue\fR
Value of the argument
.RE
.TP
\fB::math::trig::acotan\fR \fIvalue\fR
Calculate the arc cotangent of the value
.RS
.TP
float \fIvalue\fR
Value of the argument
.RE
.PP
The following hyperbolic and inverse hyperbolic functions are defined:
.TP
\fB::math::trig::cosech\fR \fIvalue\fR
Calculate the hyperbolic cosecant of the value (1/sinh(value))
.RS
.TP
float \fIvalue\fR
Value of the argument
.RE
.TP
\fB::math::trig::sech\fR \fIvalue\fR
Calculate the hyperbolic secant of the value (1/cosh(value))
.RS
.TP
float \fIvalue\fR
Value of the argument
.RE
.TP
\fB::math::trig::cotanh\fR \fIvalue\fR
Calculate the hyperbolic cotangent of the value (1/tanh(value))
.RS
.TP
float \fIvalue\fR
Value of the argument
.RE
.TP
\fB::math::trig::asinh\fR \fIvalue\fR
Calculate the arc hyperbolic sine of the value
.RS
.TP
float \fIvalue\fR
Value of the argument
.RE
.TP
\fB::math::trig::acosh\fR \fIvalue\fR
Calculate the arc hyperbolic cosine of the value
.RS
.TP
float \fIvalue\fR
Value of the argument
.RE
.TP
\fB::math::trig::atanh\fR \fIvalue\fR
Calculate the arc hyperbolic tangent of the value
.RS
.TP
float \fIvalue\fR
Value of the argument
.RE
.TP
\fB::math::trig::acosech\fR \fIvalue\fR
Calculate the arc hyperbolic cosecant of the value
.RS
.TP
float \fIvalue\fR
Value of the argument
.RE
.TP
\fB::math::trig::asech\fR \fIvalue\fR
Calculate the arc hyperbolic secant of the value
.RS
.TP
float \fIvalue\fR
Value of the argument
.RE
.TP
\fB::math::trig::acotanh\fR \fIvalue\fR
Calculate the arc hyperbolic cotangent of the value
.RS
.TP
float \fIvalue\fR
Value of the argument
.RE
.PP
The following versions of the common trigonometric functions and their
inverses are defined:
.TP
\fB::math::trig::sind\fR \fIangle\fR
Calculate the sine of the angle (in degrees)
.RS
.TP
float \fIangle\fR
Angle (in degrees)
.RE
.TP
\fB::math::trig::cosd\fR \fIangle\fR
Calculate the cosine of the angle (in degrees)
.RS
.TP
float \fIangle\fR
Angle (in radians)
.RE
.TP
\fB::math::trig::tand\fR \fIangle\fR
Calculate the cotangent of the angle (in degrees)
.RS
.TP
float \fIangle\fR
Angle (in degrees)
.RE
.TP
\fB::math::trig::cosecd\fR \fIangle\fR
Calculate the cosecant of the angle (in degrees)
.RS
.TP
float \fIangle\fR
Angle (in degrees)
.RE
.TP
\fB::math::trig::secd\fR \fIangle\fR
Calculate the secant of the angle (in degrees)
.RS
.TP
float \fIangle\fR
Angle (in degrees)
.RE
.TP
\fB::math::trig::cotand\fR \fIangle\fR
Calculate the cotangent of the angle (in degrees)
.RS
.TP
float \fIangle\fR
Angle (in degrees)
.RE
.PP
.SH "BUGS, IDEAS, FEEDBACK"
This document, and the package it describes, will undoubtedly contain
bugs and other problems\&.
Please report such in the category \fImath :: trig\fR of the
\fITcllib Trackers\fR [http://core\&.tcl\&.tk/tcllib/reportlist]\&.
Please also report any ideas for enhancements you may have for either
package and/or documentation\&.
.PP
When proposing code changes, please provide \fIunified diffs\fR,
i\&.e the output of \fBdiff -u\fR\&.
.PP
Note further that \fIattachments\fR are strongly preferred over
inlined patches\&. Attachments can be made by going to the \fBEdit\fR
form of the ticket immediately after its creation, and then using the
left-most button in the secondary navigation bar\&.
.SH KEYWORDS
math, trigonometry
.SH CATEGORY
Mathematics
.SH COPYRIGHT
.nf
Copyright (c) 2018 Arjen Markus

.fi

'\"
'\" Generated from file 'namespacex\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 200? Neil Madden (http://wiki\&.tcl\&.tk/12790)
'\" Copyright (c) 200? Various (http://wiki\&.tcl\&.tk/1489)
'\" Copyright (c) 2010 Documentation, Andreas Kupries
'\"
.TH "namespacex" n 0\&.2 tcllib "Namespace utility commands"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

..
.BS
.SH NAME
namespacex \- Namespace utility commands
.SH SYNOPSIS
package require \fBTcl  8\&.5\fR
.sp
package require \fBnamespacex  ?0\&.2?\fR
.sp
\fB::namespacex hook add\fR ?\fInamespace\fR? \fIcmdprefix\fR
.sp
\fB::namespacex hook proc\fR ?\fInamespace\fR? \fIarguments\fR \fIbody\fR
.sp
\fB::namespacex hook on\fR ?\fInamespace\fR? \fIguardcmdprefix\fR \fIactioncmdprefix\fR
.sp
\fB::namespacex hook next\fR \fIarg\fR\&.\&.\&.
.sp
\fB::namespacex import fromns\fR \fIcmdname ?\fInewname\fR \&.\&.\&.?\fR
.sp
\fB::namespacex info allchildren\fR \fInamespace\fR
.sp
\fB::namespacex info allvars\fR \fInamespace\fR
.sp
\fB::namespacex normalize\fR \fInamespace\fR
.sp
\fB::namespacex info vars\fR \fInamespace\fR ?\fIpattern\fR?
.sp
\fB::namespacex state get\fR \fInamespace\fR
.sp
\fB::namespacex state set\fR \fInamespace\fR \fIdict\fR
.sp
\fB::namespacex state drop\fR \fInamespace\fR
.sp
\fB::namespacex strip\fR \fIprefix\fR \fInamespaces\fR
.sp
.BE
.SH DESCRIPTION
This package provides a number of utility commands for working with
namespaces\&.
The commands fall into four categories:
.IP [1]
Hook commands provide and manipulate a chain of commands which
replaces the single regular \fBnamespace unknown\fR handler\&.
.IP [2]
An import command provides the ability to import any command
from another namespace\&.
.IP [3]
Information commands allow querying of variables and child
namespaces\&.
.IP [4]
State commands provide a means to serialize variable values in
a namespace\&.
.PP
.SH COMMANDS
.TP
\fB::namespacex hook add\fR ?\fInamespace\fR? \fIcmdprefix\fR
Adds the \fIcmdprefix\fR to the chain of unknown command handlers that
are invoked when the \fInamespace\fR would otherwise invoke its
unknown handler\&.
If \fInamespace\fR is not specified, then \fIcmdprefix\fR is added to
the chain of handlers for the namespace of the caller\&.
.sp
The chain of \fIcmdprefix\fR are executed in reverse order of
addition, \fIi\&.e\&.\fR the most recently added \fIcmdprefix\fR is
executed first\&.
When executed, \fIcmdprefix\fR has additional arguments appended to it
as would any namespace unknown handler\&.
.TP
\fB::namespacex hook proc\fR ?\fInamespace\fR? \fIarguments\fR \fIbody\fR
Adds an anonymous procedure to the chain of namespace unknown handlers
for the \fInamespace\fR\&.
.sp
If \fInamespace\fR is not specified, then the handler is added
to the chain of handlers for the namespace of the caller\&.
.sp
The \fIarguments\fR and \fIbody\fR are specified as for the
core \fBproc\fR command\&.
.TP
\fB::namespacex hook on\fR ?\fInamespace\fR? \fIguardcmdprefix\fR \fIactioncmdprefix\fR
Adds a guarded action to the chain of namespace unknown handlers for
the \fInamespace\fR\&.
.sp
If \fInamespace\fR is not specified, then the handler is added
to the chain of handlers for the namespace of the caller\&.
.sp
The \fIguardcmdprefix\fR is executed first\&. If it returns a
value that can be interpreted as false, then the next unknown hander
in the chain is executed\&. Otherwise, \fIactioncmdprefix\fR is executed
and the return value of the handler is the value returned by
\fIactioncmdprefix\fR\&.
.sp
When executed, both \fIguardcmdprefix\fR and
\fIactioncmdprefix\fR have the same additional arguments appended as
for any namespace unknown handler\&.
.TP
\fB::namespacex hook next\fR \fIarg\fR\&.\&.\&.
This command is available to namespace hooks to execute the next hook
in the chain of handlers for the namespace\&.
.TP
\fB::namespacex import fromns\fR \fIcmdname ?\fInewname\fR \&.\&.\&.?\fR
Imports the command \fIcmdname\fR from the \fIfromns\fR namespace into
the namespace of the caller\&.
The \fIcmdname\fR command is imported even if the \fIfromns\fR did not
originally export the command\&.
.sp
If \fInewname\fR is specified, then the imported command will
be known by that name\&. Otherwise, the command retains is original name
as given by \fIcmdname\fR\&.
.sp
Additional pairs of \fIcmdname\fR / \fInewname\fR arguments may
also be specified\&.
.TP
\fB::namespacex info allchildren\fR \fInamespace\fR
Returns a list containing the names of all child namespaces in the
specified \fInamespace\fR and its children\&. The names are all fully
qualified\&.
.TP
\fB::namespacex info allvars\fR \fInamespace\fR
Returns a list containing the names of all variables in the specified
\fInamespace\fR and its children\&. The names are all given relative to
\fInamespace\fR, and \fInot\fR fully qualified\&.
.TP
\fB::namespacex normalize\fR \fInamespace\fR
Returns the absolute name of \fInamespace\fR, which is resolved
relative to the namespace of the caller, with all unneeded colon
characters removed\&.
.TP
\fB::namespacex info vars\fR \fInamespace\fR ?\fIpattern\fR?
Returns a list containing the names of all variables in
the specified \fInamespace\fR\&.
If the \fIpattern\fR argument is specified, then only variables
matching \fIpattern\fR are returned\&. Matching is determined using the
same rules as for \fBstring match\fR\&.
.TP
\fB::namespacex state get\fR \fInamespace\fR
Returns a dictionary holding the names and values of all variables in
the specified \fInamespace\fR and its child namespaces\&.
.sp
Note that the names are all relative to \fInamespace\fR, and
\fInot\fR fully qualified\&.
.TP
\fB::namespacex state set\fR \fInamespace\fR \fIdict\fR
Takes a dictionary holding the names and values for a set of variables
and replaces the current state of the specified \fInamespace\fR and
its child namespaces with this state\&.
The result of the command is the empty string\&.
.TP
\fB::namespacex state drop\fR \fInamespace\fR
Unsets all variables in the specified \fInamespace\fR and its child
namespaces\&.
The result of the command is the empty string\&.
.TP
\fB::namespacex strip\fR \fIprefix\fR \fInamespaces\fR
Each item in \fInamespaces\fR must be the absolute normalized name of
a child namespace of namespace \fIprefix\fR\&.
Returns the corresponding list of relative names of child namespaces\&.
.PP
.SH "BUGS, IDEAS, FEEDBACK"
This document, and the package it describes, will undoubtedly contain
bugs and other problems\&.
Please report such in the category \fInamespacex\fR of the
\fITcllib Trackers\fR [http://core\&.tcl\&.tk/tcllib/reportlist]\&.
Please also report any ideas for enhancements you may have for either
package and/or documentation\&.
.PP
When proposing code changes, please provide \fIunified diffs\fR,
i\&.e the output of \fBdiff -u\fR\&.
.PP
Note further that \fIattachments\fR are strongly preferred over
inlined patches\&. Attachments can be made by going to the \fBEdit\fR
form of the ticket immediately after its creation, and then using the
left-most button in the secondary navigation bar\&.
.SH KEYWORDS
extended namespace, info, namespace unknown, namespace utilities, state (de)serialization, unknown hooking, utilities
.SH COPYRIGHT
.nf
Copyright (c) 200? Neil Madden (http://wiki\&.tcl\&.tk/12790)
Copyright (c) 200? Various (http://wiki\&.tcl\&.tk/1489)
Copyright (c) 2010 Documentation, Andreas Kupries

.fi

\fB::nameserv::configure\fR
In this form the command returns a dictionary of all supported
options, and their current values\&. The list of supported options and
their meaning can be found in section \fBOPTIONS\fR\&.
.TP
\fB::nameserv::configure\fR \fB-option\fR
In this form the command is an alias for
"\fB::nameserv::cget\fR \fB-option\fR"\&.
The list of supported options and their meaning can be found in
section \fBOPTIONS\fR\&.
.TP
\fB::nameserv::configure\fR \fB-option\fR \fIvalue\fR\&.\&.\&.
In this form the command is used to configure one or more of the
supported options\&. At least one option has to be specified, and each
option is followed by its new value\&.

\fB::nameserv::server::configure\fR
In this form the command returns a dictionary of all supported
options, and their current values\&. The list of supported options and
their meaning can be found in section \fBOPTIONS\fR\&.
.TP
\fB::nameserv::server::configure\fR \fB-option\fR
In this form the command is an alias for
"\fB::nameserv::server::cget\fR \fB-option\fR"\&.
The list of supported options and their meaning can be found in
section \fBOPTIONS\fR\&.
.TP
\fB::nameserv::server::configure\fR \fB-option\fR \fIvalue\fR\&.\&.\&.
In this form the command is used to configure one or more of the
supported options\&. At least one option has to be specified, and each
option is followed by its new value\&.

'\"
'\" Generated from file 'png\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2004, Code: Aaron Faupell <afaupell@users\&.sourceforge\&.net>
'\" Copyright (c) 2004, Doc: Andreas Kupries <andreas_kupries@users\&.sourceforge\&.net>
'\"
.TH "png" n 0\&.3 tcllib "Image manipulation"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

.SH NAME
png \- PNG querying and manipulation of meta data
.SH SYNOPSIS
package require \fBTcl  8\&.2\fR
.sp
package require \fBcrc32 \fR
.sp
package require \fBpng  ?0\&.3?\fR
.sp
\fB::png::validate\fR \fIfile\fR
.sp
\fB::png::isPNG\fR \fIfile\fR
.sp
\fB::png::imageInfo\fR \fIfile\fR
.sp
\fB::png::getTimestamp\fR \fIfile\fR
.sp
\fB::png::setTimestamp\fR \fIfile\fR \fItime\fR
.sp
\fB::png::getComments\fR \fIfile\fR
.sp
\fB::png::removeComments\fR \fIfile\fR
.sp
\fB::png::addComment\fR \fIfile\fR \fIkeyword\fR \fItext\fR
.sp
\fB::png::addComment\fR \fIfile\fR \fIkeyword\fR \fIlang\fR \fIkeyword2\fR \fItext\fR
.sp
\fB::png::getPixelDimension\fR \fIfile\fR
.sp
\fB::png::image\fR \fIfile\fR
.sp
\fB::png::write\fR \fIfile\fR \fIdata\fR
.sp
.BE
.SH DESCRIPTION

Adds a unicode (international) comment to the PNG image in \fIfile\fR,
just before the first data chunk\&. Will throw an error if no data chunk
is found\&. \fIkeyword\fR has to be less than 80 characters long to
conform to the PNG specification\&. \fIkeyword2\fR is the translated
\fIkeyword\fR, in the language specified by the language identifier
\fIlang\fR\&.
.TP
\fB::png::getPixelDimension\fR \fIfile\fR
Returns a dictionary with keys \fBppux\fR, \fBppuy\fR and
\fBunit\fR if the information is present\&.  Otherwise, it returns the empty
string\&.
.sp
The values of \fBppux\fR and \fBppuy\fR return the pixel
per unit value in X or Y direction\&.
.sp
The allowed values for key \fBunit\fR are \fBmeter\fR and
\fBunknown\fR\&. In the case of meter, the dpi value can be calculated
by multiplying with the conversion factor \fB0\&.0254\fR\&.
.TP
\fB::png::image\fR \fIfile\fR
Given a PNG file returns the image in the list of scanlines format used by Tk_GetColor\&.
.TP
\fB::png::write\fR \fIfile\fR \fIdata\fR
Takes a list of scanlines in the Tk_GetColor format and writes the represented image
to \fIfile\fR\&.
.PP

Here we describe the interface which has to be provided by the storage
callback so that pop3 servers following the interface of this module
are able to use it\&. The \fImbox\fR argument is the storage reference
as returned by the \fBlookup\fR method of the authentication
command, see section \fBAuthentication\fR\&.
.TP
\fIstorageCmd\fR \fBdele\fR \fImbox\fR \fImsgList\fR

Deletes the messages whose numeric ids are contained in the
\fImsgList\fR from the mailbox specified via \fImbox\fR\&.
.TP
\fIstorageCmd\fR \fBlock\fR \fImbox\fR
This method locks the specified mailbox for use by a single connection
to the server\&. This is necessary to prevent havoc if several
connections to the same mailbox are open\&. The complementary method is

'\"
'\" Generated from file 'pt_peg_op\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2009 Andreas Kupries <andreas_kupries@users\&.sourceforge\&.net>
'\"
.TH "pt_peg_op" i 1\&.1\&.0 tcllib "Parser Tools"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

..
.BS
.SH NAME
pt_peg_op \- Parser Tools PE Grammar Utility Operations
.SH SYNOPSIS
package require \fBTcl  8\&.5\fR
.sp
package require \fBpt::peg::op  ?1\&.1\&.0?\fR
.sp
\fB::peg::peg::op\fR \fBcalled\fR \fIcontainer\fR
.sp
\fB::peg::peg::op\fR \fBdechain\fR \fIcontainer\fR
.sp
\fB::peg::peg::op\fR \fBdrop unreachable\fR \fIcontainer\fR
.sp

\fBvalidate_recipient\fR callback
The validate_recipient callback is similar to the validate_sender
callback and permits you to verify a local mailbox and accept mail for
a local user address during RCPT command handling\&. To reject mail,
throw an error as above\&. The error message is ignored\&.
.TP
\fBdeliverMIME\fR callback

The deliverMIME callback is called once a mail message has been
successfully passed to the server\&. A mime token is constructed from
the sender, recipients and data and the users procedure it called with
this single argument\&. When the call returns, the mime token is cleaned
up so if the user wishes to preserve the data she must make a copy\&.
.sp
.CS

the validity of the value passed to the \fBset-\fBoption\fR\fR
procedure, which should throw an error (for example by using the Tcl
error command) if the value is invalid\&.
.sp
The switched layer also keeps track of the options current
values, so that a \fBset-\fBoption\fR\fR procedure is called
only when the corresponding option value passed as parameter is
different from the current value (see \fB-option\fR data members
description)\&.
.TP
\fB-option\fR
.sp
The \fB-option\fR data member is an options current value\&.
There is one for each option listed in the options procedure\&. It is a
read-only value which the switched layer checks against when an option
is changed\&.
It is rarely used at the layer derived from switched, except in the
few cases, such as in the following example:
.sp
.CS

.CE
.sp
In this case, the manufacturer's name is stored at the switched
layer level (this is why the set-manufacturer procedure has nothing to
do) and later retrieved in the printData procedure\&.
.TP
\fBcomplete\fR
.sp
The \fBcomplete\fR data member (not to be confused with the
\fBcomplete\fR procedure) is a boolean\&.
Its initial value is \fBfalse\fR and it is set to \fBtrue\fR at
the very end of the switched \fBcomplete\fR procedure\&.
It becomes useful when some options should be set at construction time
only and not dynamically, as the following example shows:
.sp
.CS

'\"
'\" Generated from file 'disjointset\&.man' by tcllib/doctools with format 'nroff'
'\"
.TH "struct::disjointset" n 1\&.1 tcllib "Tcl Data Structures"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

.de MT
.QW ""
..
.BS
.SH NAME
struct::disjointset \- Disjoint set data structure
.SH SYNOPSIS
package require \fBTcl  8\&.6\fR
.sp
package require \fBstruct::disjointset  ?1\&.1?\fR
.sp
\fB::struct::disjointset\fR \fIdisjointsetName\fR
.sp
\fIdisjointsetName\fR \fIoption\fR ?\fIarg arg \&.\&.\&.\fR?
.sp
\fIdisjointsetName\fR \fBadd-element\fR \fIitem\fR
.sp
\fIdisjointsetName\fR \fBadd-partition\fR \fIelements\fR
.sp
\fIdisjointsetName\fR \fBpartitions\fR
.sp
\fIdisjointsetName\fR \fBnum-partitions\fR
.sp
\fIdisjointsetName\fR \fBequal\fR \fIa\fR \fIb\fR
.sp
\fIdisjointsetName\fR \fBmerge\fR \fIa\fR \fIb\fR
.sp
\fIdisjointsetName\fR \fBfind\fR \fIe\fR
.sp
\fIdisjointsetName\fR \fBexemplars\fR
.sp
\fIdisjointsetName\fR \fBfind-exemplar\fR \fIe\fR
.sp
\fIdisjointsetName\fR \fBdestroy\fR
.sp
.BE
.SH DESCRIPTION
.PP
This package provides \fIdisjoint sets\fR\&. An alternative name for
this kind of structure is \fImerge-find\fR\&.

.RS
.TP
\fIdisjointsetName\fR \fIoption\fR ?\fIarg arg \&.\&.\&.\fR?
The \fBoption\fR and the \fIarg\fRs determine the exact behavior of
the command\&. The following commands are possible for disjointset
objects:
.RE
.TP
\fIdisjointsetName\fR \fBadd-element\fR \fIitem\fR
Creates a new partition in the specified disjoint set, and fills it
with the single item \fIitem\fR\&.  The command maintains
the integrity of the disjoint set, i\&.e\&. it verifies that none of the
\fIelements\fR are already part of the disjoint set and throws an
error otherwise\&.
.sp
The result of this method is the empty string\&.
.sp
This method runs in constant time\&.
.TP
\fIdisjointsetName\fR \fBadd-partition\fR \fIelements\fR
Creates a new partition in specified disjoint set, and fills it with
the values found in the set of \fIelements\fR\&. The command maintains
the integrity of the disjoint set, i\&.e\&. it verifies that none of the
\fIelements\fR are already part of the disjoint set and throws an
error otherwise\&.
.sp
The result of the command is the empty string\&.
.sp
This method runs in time proportional to the size of \fIelements\fR]\&.
.TP
\fIdisjointsetName\fR \fBpartitions\fR
Returns the set of partitions the named disjoint set currently
consists of\&. The form of the result is a list of lists; the inner
lists contain the elements of the partitions\&.
.sp
This method runs in time O(N*alpha(N)),
where N is the number of elements in the disjoint set and alpha
is the inverse Ackermann function\&.
.TP
\fIdisjointsetName\fR \fBnum-partitions\fR
Returns the number of partitions the named disjoint set currently
consists of\&.
.sp
This method runs in constant time\&.
.TP
\fIdisjointsetName\fR \fBequal\fR \fIa\fR \fIb\fR
Determines if the two elements \fIa\fR and \fIb\fR of the disjoint set
belong to the same partition\&. The result of the method is a boolean
value, \fBTrue\fR if the two elements are contained in the same
partition, and \fBFalse\fR otherwise\&.
.sp
An error will be thrown if either \fIa\fR or \fIb\fR are not elements
of the disjoint set\&.
.sp
This method runs in amortized time O(alpha(N)), where N is the number of
elements in the larger partition and alpha is the inverse Ackermann function\&.
.TP
\fIdisjointsetName\fR \fBmerge\fR \fIa\fR \fIb\fR
Determines the partitions the elements \fIa\fR and \fIb\fR are
contained in and merges them into a single partition\&.  If the two
elements were already contained in the same partition nothing will
change\&.
.sp
The result of the method is the empty string\&.
.sp
This method runs in amortized time O(alpha(N)), where N is the number of
items in the larger of the partitions being merged\&. The worst case time
is O(N)\&.
.TP
\fIdisjointsetName\fR \fBfind\fR \fIe\fR
Returns a list of the members of the partition of the disjoint set
which contains the element
\fIe\fR\&.
.sp
This method runs in O(N*alpha(N)) time, where N is the total number of
items in the disjoint set and alpha is the inverse Ackermann function,
See \fBfind-exemplar\fR for a faster method, if all that is needed
is a unique identifier for the partition, rather than an enumeration
of all its elements\&.
.TP
\fIdisjointsetName\fR \fBexemplars\fR
Returns a list containing an exemplar of each partition in the disjoint
set\&. The exemplar is a member of the partition, chosen arbitrarily\&.
.sp
This method runs in O(N*alpha(N)) time, where N is the total number of items
in the disjoint set and alpha is the inverse Ackermann function\&.
.TP
\fIdisjointsetName\fR \fBfind-exemplar\fR \fIe\fR
Returns the exemplar of the partition of the disjoint set containing
the element \fIe\fR\&.  Throws an error if \fIe\fR is not found in the
disjoint set\&.  The exemplar is an arbitrarily chosen member of the partition\&.
The only operation that will change the exemplar of any partition is
\fBmerge\fR\&.
.sp
This method runs in O(alpha(N)) time, where N is the number of items in
the partition containing E, and alpha is the inverse Ackermann function\&.
.TP
\fIdisjointsetName\fR \fBdestroy\fR
Destroys the disjoint set object and all associated memory\&.
.PP
.SH "BUGS, IDEAS, FEEDBACK"
This document, and the package it describes, will undoubtedly contain
bugs and other problems\&.

.de MT
.QW ""
..
.BS
.SH NAME
struct::graph::op \- Operation for (un)directed graph objects
.SH SYNOPSIS
package require \fBTcl  8\&.6\fR
.sp
package require \fBstruct::graph::op  ?0\&.11\&.3?\fR
.sp
\fBstruct::graph::op::toAdjacencyMatrix\fR \fIg\fR
.sp
\fBstruct::graph::op::toAdjacencyList\fR \fIG\fR ?\fIoptions\fR\&.\&.\&.?
.sp

'\"
'\" Generated from file 'struct_list\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2003-2005 by Kevin B\&. Kenny\&. All rights reserved
'\" Copyright (c) 2003-2012 Andreas Kupries <andreas_kupries@users\&.sourceforge\&.net>
'\"
.TH "struct::list" n 1\&.8\&.4 tcllib "Tcl Data Structures"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

..
.BS
.SH NAME
struct::list \- Procedures for manipulating lists
.SH SYNOPSIS
package require \fBTcl  8\&.4\fR
.sp
package require \fBstruct::list  ?1\&.8\&.4?\fR
.sp
\fB::struct::list\fR \fBlongestCommonSubsequence\fR \fIsequence1\fR \fIsequence2\fR ?\fImaxOccurs\fR?
.sp
\fB::struct::list\fR \fBlongestCommonSubsequence2\fR \fIsequence1 sequence2\fR ?\fImaxOccurs\fR?
.sp
\fB::struct::list\fR \fBlcsInvert\fR \fIlcsData\fR \fIlen1\fR \fIlen2\fR
.sp

The following parameters are provided to this procedure:
.RS
.TP
\fIName\fR
Name of the argument
.TP
\fIIsOptional\fR
If true (=\fB1\fR) the argument is optional which should be indicated by the generated string (for example by putting the argument into brackets {[]} or into question marks '?'):
.CS

gen(TXT,ArgumentString) mtype 1 0 string -> \fI"[mtype]"\fR
.CE
.TP
\fIIsNamed\fR
If true (=\fB1\fR) an argument is a named argument (option)\&. The generated string should in this case contain the argument/option name, followed by the argument itself:

The name of the first unnamed argument has therefore not to start with the '-' character\&. The unnamed argument is otherwise considered as name of another named argument\&. This is especially important if the first unnamed argument is given by a variable that can contain any character strings:
.CS

my_proc \fB-n1 N1 -n2 N2 "->" "<-"\fR
\fI-> my_proc: Argument '->' not known\fR

set U1 "->"
my_proc \fB-n1 N1 -n2 N2 $U1 U2\fR
my_proc: Argument '->' not known
.CE
The '--' flag allows separating unambiguously the unnamed arguments from the named arguments\&. All data after the '--' flag will be considered as unnamed argument:
.CS

my_proc \fB-n1 N1 -n2 N2 -- "->" "<-"\fR
\fI-> n1:'N1', n2:'N2', u1:'->', u2:'<-'\fR

.RE
.TP
\fB-length\fR \fIinteger\fR
Set the length of the \fIlogical\fR line in the string to
\fIinteger\fR\&.  \fIinteger\fR must be a positive integer
value\&. Defaults to \fB72\fR\&.
.TP
\fB-strictlength\fR \fIboolean\fR

If set to \fBfalse\fR (default), a line can exceed the specified
\fB-length\fR if a single word is longer than \fB-length\fR\&. If
set to \fBtrue\fR, words that are longer than \fB-length\fR are
split so that no line exceeds the specified \fB-length\fR\&.
.RE
.TP
\fB::textutil::adjust::readPatterns\fR \fIfilename\fR

This command registers the (accept) socket \fIsock\fR as the
identifier fo an HTTP server that is capable of doing WebSockets\&.
Paths onto which this server will listen for incoming connections
should be declared using \fB::websocket::live\fR\&.
.TP
\fB::websocket::live\fR \fIsock\fR \fIpath\fR \fIcb\fR ?\fIproto\fR?
This procedure registers callbacks that will be performed on a
WebSocket compliant server registered with \fB::websocket::server\fR
whenever a client connects to a matching path and protocol\&.
\fIsock\fR is the listening socket of the websocket compliant server
declared using \fB::websocket::server\fR\&.  \fIpath\fR is a glob-style
path to match in client request, whenever this will occur\&.  \fIcb\fR
is the command to callback (see Callbacks)\&.  \fIproto\fR is a
glob-style protocol name matcher\&.
.TP

math::polynomials
.TP
\fBfiles/modules/math/rational_funcs\&.n\fR
math::rationalfunctions
.TP
\fBfiles/modules/math/special\&.n\fR
math::special
.TP
\fBfiles/modules/math/trig\&.n\fR
math::trig
.TP
\fBfiles/modules/simulation/annealing\&.n\fR
simulation::annealing
.TP
\fBfiles/modules/simulation/montecarlo\&.n\fR
simulation::montecarlo
.TP

page_util_norm_peg
.RE
TreeQL
.RS
.TP
\fBfiles/modules/treeql/treeql\&.n\fR
treeql
.RE
trigonometry
.RS
.TP
\fBfiles/modules/math/trig\&.n\fR
math::trig
.RE
trimming
.RS
.TP
\fBfiles/modules/textutil/textutil\&.n\fR
textutil
.TP

.TP
\fBjson::write\fR
\fIfiles/modules/json/json_write\&.n\fR: JSON generation
.TP
\fBlambda\fR
\fIfiles/modules/lambda/lambda\&.n\fR: Utility commands for anonymous procedures
.TP
\fBlazyset\fR
\fIfiles/modules/lazyset/lazyset\&.n\fR: Lazy evaluation
.TP
\fBldap\fR
\fIfiles/modules/ldap/ldap\&.n\fR: LDAP client
.TP
\fBldapx\fR
\fIfiles/modules/ldap/ldapx\&.n\fR: LDAP extended object interface
.TP
\fBlog\fR

.TP
\fBmath::special\fR
\fIfiles/modules/math/special\&.n\fR: Special mathematical functions
.TP
\fBmath::statistics\fR
\fIfiles/modules/math/statistics\&.n\fR: Basic statistical functions and procedures
.TP
\fBmath::trig\fR
\fIfiles/modules/math/trig\&.n\fR: Trigonometric anf hyperbolic functions
.TP
\fBmd4\fR
\fIfiles/modules/md4/md4\&.n\fR: MD4 Message-Digest Algorithm
.TP
\fBmd5\fR
\fIfiles/modules/md5/md5\&.n\fR: MD5 Message-Digest Algorithm
.TP
\fBmd5crypt\fR

<td class="#doctools_idxleft" width="35%"><a name="matching"> matching </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/grammar_me/me_intro.html"> grammar::me_intro </a> &#183; <a href="tcllib/files/modules/grammar_peg/peg_interp.html"> grammar::peg::interp </a> &#183; <a href="tcllib/files/apps/pt.html"> pt </a> &#183; <a href="tcllib/files/modules/pt/pt_astree.html"> pt::ast </a> &#183; <a href="tcllib/files/modules/pt/pt_cparam_config_critcl.html"> pt::cparam::configuration::critcl </a> &#183; <a href="tcllib/files/modules/pt/pt_cparam_config_tea.html"> pt::cparam::configuration::tea </a> &#183; <a href="tcllib/files/modules/pt/pt_json_language.html"> pt::json_language </a> &#183; <a href="tcllib/files/modules/pt/pt_param.html"> pt::param </a> &#183; <a href="tcllib/files/modules/pt/pt_pexpression.html"> pt::pe </a> &#183; <a href="tcllib/files/modules/pt/pt_pexpr_op.html"> pt::pe::op </a> &#183; <a href="tcllib/files/modules/pt/pt_pegrammar.html"> pt::peg </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_container.html"> pt::peg::container </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_container_peg.html"> pt::peg::container::peg </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_export.html"> pt::peg::export </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_export_container.html"> pt::peg::export::container </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_export_json.html"> pt::peg::export::json </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_export_peg.html"> pt::peg::export::peg </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_from_container.html"> pt::peg::from::container </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_from_json.html"> pt::peg::from::json </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_from_peg.html"> pt::peg::from::peg </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_import.html"> pt::peg::import </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_import_container.html"> pt::peg::import::container </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_import_json.html"> pt::peg::import::json </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_import_peg.html"> pt::peg::import::peg </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_interp.html"> pt::peg::interp </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_to_container.html"> pt::peg::to::container </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_to_cparam.html"> pt::peg::to::cparam </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_to_json.html"> pt::peg::to::json </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_to_param.html"> pt::peg::to::param </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_to_peg.html"> pt::peg::to::peg </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_to_tclparam.html"> pt::peg::to::tclparam </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_language.html"> pt::peg_language </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_introduction.html"> pt::pegrammar </a> &#183; <a href="tcllib/files/modules/pt/pt_pgen.html"> pt::pgen </a> &#183; <a href="tcllib/files/modules/pt/pt_rdengine.html"> pt::rde </a> &#183; <a href="tcllib/files/modules/pt/pt_tclparam_config_nx.html"> pt::tclparam::configuration::nx </a> &#183; <a href="tcllib/files/modules/pt/pt_tclparam_config_snit.html"> pt::tclparam::configuration::snit </a> &#183; <a href="tcllib/files/modules/pt/pt_tclparam_config_tcloo.html"> pt::tclparam::configuration::tcloo </a> &#183; <a href="tcllib/files/modules/pt/pt_util.html"> pt::util </a> &#183; <a href="tcllib/files/modules/pt/pt_to_api.html"> pt_export_api </a> &#183; <a href="tcllib/files/modules/pt/pt_from_api.html"> pt_import_api </a> &#183; <a href="tcllib/files/modules/pt/pt_introduction.html"> pt_introduction </a> &#183; <a href="tcllib/files/modules/pt/pt_parse_peg.html"> pt_parse_peg </a> &#183; <a href="tcllib/files/modules/pt/pt_parser_api.html"> pt_parser_api </a> &#183; <a href="tcllib/files/modules/pt/pt_peg_op.html"> pt_peg_op </a> &#183; <a href="tcllib/files/modules/struct/graphops.html"> struct::graph::op </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="math"> math </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/math/math.html"> math </a> &#183; <a href="tcllib/files/modules/math/bigfloat.html"> math::bigfloat </a> &#183; <a href="tcllib/files/modules/math/bignum.html"> math::bignum </a> &#183; <a href="tcllib/files/modules/math/calculus.html"> math::calculus </a> &#183; <a href="tcllib/files/modules/math/qcomplex.html"> math::complexnumbers </a> &#183; <a href="tcllib/files/modules/math/constants.html"> math::constants </a> &#183; <a href="tcllib/files/modules/math/decimal.html"> math::decimal </a> &#183; <a href="tcllib/files/modules/math/fuzzy.html"> math::fuzzy </a> &#183; <a href="tcllib/files/modules/math/math_geometry.html"> math::geometry </a> &#183; <a href="tcllib/files/modules/math/interpolate.html"> math::interpolate </a> &#183; <a href="tcllib/files/modules/math/linalg.html"> math::linearalgebra </a> &#183; <a href="tcllib/files/modules/math/optimize.html"> math::optimize </a> &#183; <a href="tcllib/files/modules/math/pca.html"> math::PCA </a> &#183; <a href="tcllib/files/modules/math/polynomials.html"> math::polynomials </a> &#183; <a href="tcllib/files/modules/math/rational_funcs.html"> math::rationalfunctions </a> &#183; <a href="tcllib/files/modules/math/special.html"> math::special </a> &#183; <a href="tcllib/files/modules/math/trig.html"> math::trig </a> &#183; <a href="tcllib/files/modules/simulation/annealing.html"> simulation::annealing </a> &#183; <a href="tcllib/files/modules/simulation/montecarlo.html"> simulation::montecarlo </a> &#183; <a href="tcllib/files/modules/simulation/simulation_random.html"> simulation::random </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="mathematics"> mathematics </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/math/fourier.html"> math::fourier </a> &#183; <a href="tcllib/files/modules/math/statistics.html"> math::statistics </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>

</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="treeql"> TreeQL </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/treeql/treeql.html"> treeql </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="trigonometry"> trigonometry </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/math/trig.html"> math::trig </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="trimming"> trimming </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/textutil/textutil.html"> textutil </a> &#183; <a href="tcllib/files/modules/textutil/trim.html"> textutil::trim </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="twitter"> twitter </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/oauth/oauth.html"> oauth </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="type"> type </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/fileutil/fileutil.html"> fileutil </a> &#183; <a href="tcllib/files/modules/fumagic/cfront.html"> fileutil::magic::cfront </a> &#183; <a href="tcllib/files/modules/fumagic/cgen.html"> fileutil::magic::cgen </a> &#183; <a href="tcllib/files/modules/fumagic/filetypes.html"> fileutil::magic::filetype </a> &#183; <a href="tcllib/files/modules/fumagic/rtcore.html"> fileutil::magic::rt </a> &#183; <a href="tcllib/files/modules/snit/snit.html"> snit </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="type_checking"> Type checking </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/valtype/valtype_common.html"> valtype::common </a> &#183; <a href="tcllib/files/modules/valtype/cc_amex.html"> valtype::creditcard::amex </a> &#183; <a href="tcllib/files/modules/valtype/cc_discover.html"> valtype::creditcard::discover </a> &#183; <a href="tcllib/files/modules/valtype/cc_mastercard.html"> valtype::creditcard::mastercard </a> &#183; <a href="tcllib/files/modules/valtype/cc_visa.html"> valtype::creditcard::visa </a> &#183; <a href="tcllib/files/modules/valtype/ean13.html"> valtype::gs1::ean13 </a> &#183; <a href="tcllib/files/modules/valtype/iban.html"> valtype::iban </a> &#183; <a href="tcllib/files/modules/valtype/imei.html"> valtype::imei </a> &#183; <a href="tcllib/files/modules/valtype/isbn.html"> valtype::isbn </a> &#183; <a href="tcllib/files/modules/valtype/luhn.html"> valtype::luhn </a> &#183; <a href="tcllib/files/modules/valtype/luhn5.html"> valtype::luhn5 </a> &#183; <a href="tcllib/files/modules/valtype/usnpi.html"> valtype::usnpi </a> &#183; <a href="tcllib/files/modules/valtype/verhoeff.html"> valtype::verhoeff </a>
</td></tr>
<tr class="#doctools_idxheader"><th colspan="2">
<a name="cU">Keywords: U</a>
</th></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="uevent"> uevent </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/hook/hook.html"> hook </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="unbind"> unbind </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/uev/uevent.html"> uevent </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="uncapitalize"> uncapitalize </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/textutil/textutil_string.html"> textutil::string </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="undenting"> undenting </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/textutil/adjust.html"> textutil::adjust </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="unicode"> unicode </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/stringprep/stringprep.html"> stringprep </a> &#183; <a href="tcllib/files/modules/stringprep/stringprep_data.html"> stringprep::data </a> &#183; <a href="tcllib/files/modules/stringprep/unicode.html"> unicode </a> &#183; <a href="tcllib/files/modules/stringprep/unicode_data.html"> unicode::data </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="union"> union </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/struct/disjointset.html"> struct::disjointset </a> &#183; <a href="tcllib/files/modules/struct/struct_set.html"> struct::set </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="unit"> unit </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/units/units.html"> units </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="unknown_hooking"> unknown hooking </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/namespacex/namespacex.html"> namespacex </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="untie"> untie </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/tie/tie_std.html"> tie </a> &#183; <a href="tcllib/files/modules/tie/tie.html"> tie </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="update"> update </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/coroutine/tcllib_coroutine.html"> coroutine </a> &#183; <a href="tcllib/files/modules/coroutine/coro_auto.html"> coroutine::auto </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="uri"> uri </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/uri/uri.html"> uri </a> &#183; <a href="tcllib/files/modules/uri/urn-scheme.html"> uri_urn </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="url"> url </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/doctools2idx/idx_container.html"> doctools::idx </a> &#183; <a href="tcllib/files/modules/doctools2idx/idx_export.html"> doctools::idx::export </a> &#183; <a href="tcllib/files/modules/doctools2idx/idx_import.html"> doctools::idx::import </a> &#183; <a href="tcllib/files/modules/doctools2toc/toc_export.html"> doctools::toc::export </a> &#183; <a href="tcllib/files/modules/doctools2toc/toc_import.html"> doctools::toc::import </a> &#183; <a href="tcllib/files/modules/map/map_geocode_nominatim.html"> map::geocode::nominatim </a> &#183; <a href="tcllib/files/modules/map/map_slippy_fetcher.html"> map::slippy::fetcher </a> &#183; <a href="tcllib/files/modules/uri/uri.html"> uri </a> &#183; <a href="tcllib/files/modules/uri/urn-scheme.html"> uri_urn </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="urn"> urn </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/uri/urn-scheme.html"> uri_urn </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="us_npi"> US-NPI </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/valtype/usnpi.html"> valtype::usnpi </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="utilities"> utilities </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/namespacex/namespacex.html"> namespacex </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="uuencode"> uuencode </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/base64/uuencode.html"> uuencode </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="uuid"> UUID </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/uuid/uuid.html"> uuid </a>
</td></tr>
<tr class="#doctools_idxheader"><th colspan="2">
<a name="cV">Keywords: V</a>
</th></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="validation"> Validation </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/valtype/valtype_common.html"> valtype::common </a> &#183; <a href="tcllib/files/modules/valtype/cc_amex.html"> valtype::creditcard::amex </a> &#183; <a href="tcllib/files/modules/valtype/cc_discover.html"> valtype::creditcard::discover </a> &#183; <a href="tcllib/files/modules/valtype/cc_mastercard.html"> valtype::creditcard::mastercard </a> &#183; <a href="tcllib/files/modules/valtype/cc_visa.html"> valtype::creditcard::visa </a> &#183; <a href="tcllib/files/modules/valtype/ean13.html"> valtype::gs1::ean13 </a> &#183; <a href="tcllib/files/modules/valtype/iban.html"> valtype::iban </a> &#183; <a href="tcllib/files/modules/valtype/imei.html"> valtype::imei </a> &#183; <a href="tcllib/files/modules/valtype/isbn.html"> valtype::isbn </a> &#183; <a href="tcllib/files/modules/valtype/luhn.html"> valtype::luhn </a> &#183; <a href="tcllib/files/modules/valtype/luhn5.html"> valtype::luhn5 </a> &#183; <a href="tcllib/files/modules/valtype/usnpi.html"> valtype::usnpi </a> &#183; <a href="tcllib/files/modules/valtype/verhoeff.html"> valtype::verhoeff </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="value_checking"> Value checking </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/valtype/valtype_common.html"> valtype::common </a> &#183; <a href="tcllib/files/modules/valtype/cc_amex.html"> valtype::creditcard::amex </a> &#183; <a href="tcllib/files/modules/valtype/cc_discover.html"> valtype::creditcard::discover </a> &#183; <a href="tcllib/files/modules/valtype/cc_mastercard.html"> valtype::creditcard::mastercard </a> &#183; <a href="tcllib/files/modules/valtype/cc_visa.html"> valtype::creditcard::visa </a> &#183; <a href="tcllib/files/modules/valtype/ean13.html"> valtype::gs1::ean13 </a> &#183; <a href="tcllib/files/modules/valtype/iban.html"> valtype::iban </a> &#183; <a href="tcllib/files/modules/valtype/imei.html"> valtype::imei </a> &#183; <a href="tcllib/files/modules/valtype/isbn.html"> valtype::isbn </a> &#183; <a href="tcllib/files/modules/valtype/luhn.html"> valtype::luhn </a> &#183; <a href="tcllib/files/modules/valtype/luhn5.html"> valtype::luhn5 </a> &#183; <a href="tcllib/files/modules/valtype/usnpi.html"> valtype::usnpi </a> &#183; <a href="tcllib/files/modules/valtype/verhoeff.html"> valtype::verhoeff </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="vectors"> vectors </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/math/linalg.html"> math::linearalgebra </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="verhoeff"> verhoeff </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/valtype/verhoeff.html"> valtype::verhoeff </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="vertex"> vertex </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/struct/graph.html"> struct::graph </a> &#183; <a href="tcllib/files/modules/struct/graphops.html"> struct::graph::op </a>
</td></tr>
<tr class="#doctools_idxodd" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="vertex_cover"> vertex cover </a></td>
<td class="#doctools_idxright" width="65%">
<a href="tcllib/files/modules/struct/graphops.html"> struct::graph::op </a>
</td></tr>
<tr class="#doctools_idxeven" valign=top>
<td class="#doctools_idxleft" width="35%"><a name="virtual_channel"> virtual channel </a></td>
<td class="#doctools_idxright" width="65%">
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<a href="tcllib/files/modules/valtype/cc_visa.html"> valtype::creditcard::visa </a>
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<!DOCTYPE html><html><head>
<title>cache::async - In-memory caches</title>
<style type="text/css"><!--
    HTML {
	background: 	#FFFFFF;
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| <a href="../../../toc.html">Table Of Contents</a>
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 ] <hr>
<div class="doctools">
<h1 class="doctools_title">cache::async(n) 0.3.1 tcllib &quot;In-memory caches&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>cache::async - Asynchronous in-memory cache</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">API</a></li>
<li class="doctools_section"><a href="#section3">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.4</b></li>
<li>package require <b class="pkgname">cache::async <span class="opt">?0.3.1?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::cache::async</b> <i class="arg">objectName</i> <i class="arg">commandprefix</i> <span class="opt">?<i class="arg">options</i>...?</span></a></li>
<li><a href="#2"><i class="arg">objectName</i> <b class="method">get</b> <i class="arg">key</i> <i class="arg">donecmdprefix</i></a></li>
<li><a href="#3"><i class="arg">objectName</i> <b class="method">set</b> <i class="arg">key</i> <i class="arg">value</i></a></li>
<li><a href="#4"><i class="arg">objectName</i> <b class="method">unset</b> <i class="arg">key</i></a></li>
<li><a href="#5"><i class="arg">objectName</i> <b class="method">exists</b> <i class="arg">key</i></a></li>

<li><a href="#5"><b class="cmd">::cron::object_coroutine</b> <i class="arg">object</i> <i class="arg">coroutine</i> <i class="arg">?info?</i></a></li>
<li><a href="#6"><b class="cmd">::cron::sleep</b> <i class="arg">milliseconds</i></a></li>
<li><a href="#7"><b class="cmd">::cron::task delete</b> <i class="arg">process</i></a></li>
<li><a href="#8"><b class="cmd">::cron::task exists</b> <i class="arg">process</i></a></li>
<li><a href="#9"><b class="cmd">::cron::task info</b> <i class="arg">process</i></a></li>
<li><a href="#10"><b class="cmd">::cron::task set</b> <i class="arg">process</i> <i class="arg">field</i> <i class="arg">value</i> <i class="arg">?field...?</i> <i class="arg">?value...?</i></a></li>
<li><a href="#11"><b class="cmd">::cron::wake</b> <i class="arg">?who?</i></a></li>
<li><a href="#12"><b class="cmd">::cron::clock_step</b> <i class="arg">milliseconds</i></a></li>
<li><a href="#13"><b class="cmd">::cron::clock_delay</b> <i class="arg">milliseconds</i></a></li>
<li><a href="#14"><b class="cmd">::cron::clock_sleep</b> <i class="arg">seconds</i> <i class="arg">?offset?</i></a></li>
<li><a href="#15"><b class="cmd">::cron::clock_set</b> <i class="arg">newtime</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>The <b class="package">cron</b> package provides a Pure-tcl set of tools to allow

<dt><a name="8"><b class="cmd">::cron::task exists</b> <i class="arg">process</i></a></dt>
<dd><p>Returns true if <i class="arg">process</i> is registered with cron.</p></dd>
<dt><a name="9"><b class="cmd">::cron::task info</b> <i class="arg">process</i></a></dt>
<dd><p>Returns a dict describing <i class="arg">process</i>. See <b class="cmd">::cron::task set</b> for a description of the options.</p></dd>
<dt><a name="10"><b class="cmd">::cron::task set</b> <i class="arg">process</i> <i class="arg">field</i> <i class="arg">value</i> <i class="arg">?field...?</i> <i class="arg">?value...?</i></a></dt>
<dd><p>If <i class="arg">process</i> does not exist, it is created. Options Include:</p>
<dl class="doctools_definitions">
<dt><b class="cmd"><a href="../../../../index.html#command">command</a></b></dt>
<dd><p>If <b class="cmd"><a href="../coroutine/tcllib_coroutine.html">coroutine</a></b> is black, a global command which implements this process. If <b class="cmd"><a href="../coroutine/tcllib_coroutine.html">coroutine</a></b> is not
black, the command to invoke to create or recreate the coroutine.</p></dd>
<dt><b class="cmd"><a href="../coroutine/tcllib_coroutine.html">coroutine</a></b></dt>
<dd><p>The name of the coroutine (if any) which implements this process.</p></dd>
<dt><b class="cmd">frequency</b></dt>
<dd><p>If -1, this process is terminated after the next event. If 0 this process should be called during every
idle event. If positive, this process should generate events periodically. The frequency is an integer number
of milliseconds between events.</p></dd>
<dt><b class="cmd"><a href="../../../../index.html#object">object</a></b></dt>
<dd><p>The object associated with this process or coroutine.</p></dd>
<dt><b class="cmd">scheduled</b></dt>
<dd><p>If non-zero, the absolute time from the epoch (in milliseconds) that this process will trigger an event.
If zero, and the <b class="cmd">frequency</b> is also zero, this process is called every idle loop.</p></dd>
<dt><b class="cmd"><a href="../../../../index.html#running">running</a></b></dt>
<dd><p>A boolean flag. If true it indicates the process never returned or yielded during the event loop,
and will not be called again until it does so.</p></dd>
</dl></dd>
<dt><a name="11"><b class="cmd">::cron::wake</b> <i class="arg">?who?</i></a></dt>
<dd><p>Wake up cron, and arrange for its event loop to be run during the next Idle cycle.</p>
<pre class="doctools_example">
::cron::wake {I just did something important}
</pre>
</dd>
</dl>
<p>Several utility commands are provided that are used internally within cron and for
testing cron, but may or may not be useful in the general cases.</p>
<dl class="doctools_definitions">
<dt><a name="12"><b class="cmd">::cron::clock_step</b> <i class="arg">milliseconds</i></a></dt>
<dd><p>Return a clock time absolute to the epoch which falls on the next
border between one second and the next for the value of <i class="arg">milliseconds</i></p></dd>
<dt><a name="13"><b class="cmd">::cron::clock_delay</b> <i class="arg">milliseconds</i></a></dt>
<dd><p>Return a clock time absolute to the epoch which falls on the next
border between one second and the next <i class="arg">milliseconds</i> in the future.</p></dd>
<dt><a name="14"><b class="cmd">::cron::clock_sleep</b> <i class="arg">seconds</i> <i class="arg">?offset?</i></a></dt>
<dd><p>Return a clock time absolute to the epoch which falls exactly <i class="arg">seconds</i> in
the future. If offset is given it may be positive or negative, and will shift
the final time to before or after the second would flip.</p></dd>
<dt><a name="15"><b class="cmd">::cron::clock_set</b> <i class="arg">newtime</i></a></dt>
<dd><p>Sets the internal clock for cron. This command will advance the time in 100ms
increment, triggering events, until the internal time catches up with <i class="arg">newtime</i>.</p>
<p><i class="arg">newtime</i> is expressed in absolute milliseconds since the beginning of the epoch.</p></dd>
</dl>
</div>
<div id="section3" class="doctools_section"><h2><a name="section3">Bugs, Ideas, Feedback</a></h2>
<p>This document, and the package it describes, will undoubtedly contain
bugs and other problems.
Please report such in the category <em>odie</em> of the
<a href="http://core.tcl.tk/tcllib/reportlist">Tcllib Trackers</a>.

<dt>varname <i class="arg">fvar</i> (in)</dt>
<dd><p>Has to refer to an array variable. Keys are strings containing
date, author of a log entry, and a comment for that entry, in this
order, separated by commas.</p>
<p>The values are lists of the files the entry is touching.</p></dd>
</dl></dd>
<dt><a name="2"><b class="cmd">::doctools::cvs::toChangeLog</b> <i class="arg">evar</i> <i class="arg">cvar</i> <i class="arg">fvar</i></a></dt>

<dd><p>The three arguments for this command are the same as the last three
arguments of the command <b class="cmd">::doctools::cvs::scanLog</b>. This command
however expects them to be filled with information about one or more
logs. It takes this information and converts it into a text in the
format of a ChangeLog as accepted and generated by <b class="syscmd"><a href="../../../../index.html#emacs">emacs</a></b>. The
constructed text is returned as the result of the command.</p></dd>
</dl>
</div>

[<b class="cmd">require   PACKAGE</b>]
[description]
[manpage_end]
</pre>
<p>Remember that the whitespace is optional. The document</p>
<pre class="doctools_example">
    [manpage_begin NAME SECTION VERSION]










    [copyright {YEAR AUTHOR}][titledesc TITLE][moddesc MODULE_TITLE]
    [require PACKAGE VERSION][require PACKAGE][description]
    [vset CATEGORY doctools]
[include ../doctools2base/include/feedback.inc]
[manpage_end]
</pre>
<p>has the same meaning as the example before.</p>

<p>The example demonstrating the use of text markup is an excerpt from
the <i class="term"><a href="doctools_lang_cmdref.html">doctools language command reference</a></i>, with some
highlighting added.
It shows their use within a block of text, as the arguments of a list
item command (<b class="cmd">call</b>), and our ability to nest them.</p>
<pre class="doctools_example">
  ...
  [call [<b class="cmd">cmd arg_def</b>] [<b class="cmd">arg type</b>] [<b class="cmd">arg name</b>] [<b class="cmd">opt</b> [<b class="cmd">arg mode</b>]]]
  Text structure. List element. Argument list. Automatically closes the
  previous list element. Specifies the data-[<b class="cmd">arg type</b>] of the described
  argument of a command, its [<b class="cmd">arg name</b>] and its i/o-[<b class="cmd">arg mode</b>]. The
  latter is optional.
  ...
</pre>
</div>

<!DOCTYPE html><html><head>
<title>lazyset - Lazy evaluation for variables and arrays</title>
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--></style>
</head>
<!-- Generated from file 'lazyset.man' by tcllib/doctools with format 'html'
   -->
<!-- Copyright &amp;copy; 2018 Roy Keene
   -->
<!-- lazyset.n
   -->
<body><hr> [
   <a href="../../../../../../../../home">Tcllib Home</a>
| <a href="../../../../toc.html">Main Table Of Contents</a>
| <a href="../../../toc.html">Table Of Contents</a>
| <a href="../../../../index.html">Keyword Index</a>
| <a href="../../../../toc0.html">Categories</a>
| <a href="../../../../toc1.html">Modules</a>
| <a href="../../../../toc2.html">Applications</a>
 ] <hr>
<div class="doctools">
<h1 class="doctools_title">lazyset(n) 1 tcllib &quot;Lazy evaluation for variables and arrays&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>lazyset - Lazy evaluation</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">COMMANDS</a></li>
<li class="doctools_section"><a href="#section3">EXAMPLES</a></li>
<li class="doctools_section"><a href="#section4">AUTHORS</a></li>
<li class="doctools_section"><a href="#section5">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.5</b></li>
<li>package require <b class="pkgname">lazyset <span class="opt">?1?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::lazyset::variable</b> <span class="opt">?<i class="arg">-array boolean</i>?</span> <span class="opt">?<i class="arg">-appendArgs boolean</i>?</span> <i class="arg">variableName</i> <i class="arg">commandPrefix</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>The <b class="package">lazyset</b> package provides a mechanism for deferring execution
of code until a specific variable or any index of an array is referenced.</p>
</div>
<div id="section2" class="doctools_section"><h2><a name="section2">COMMANDS</a></h2>
<dl class="doctools_definitions">
<dt><a name="1"><b class="cmd">::lazyset::variable</b> <span class="opt">?<i class="arg">-array boolean</i>?</span> <span class="opt">?<i class="arg">-appendArgs boolean</i>?</span> <i class="arg">variableName</i> <i class="arg">commandPrefix</i></a></dt>
<dd><p>Arrange for the code specified as <i class="arg">commandPrefix</i> to be executed when
the variable whose name is specified by <i class="arg">variableName</i> is read for
the first time.
If the optional argument <i class="arg">-array boolean</i> is specified as true,
then the variable specified as <i class="arg">variableName</i> is treated as an
array and attempting to read any index of the array causes that
index to be set by the <i class="arg">commandPrefix</i> as they are read.
If the optional argument <i class="arg">-appendArgs boolean</i> is specified as
false, then the variable name and subnames are not appended to the
<i class="arg">commandPrefix</i> before it is evaluated.  If the argument
<i class="arg">-appendArgs boolean</i> is not specified or is specified as true
then 1 or 2 additional arguments are appended to the <i class="arg">commandPrefix</i>.
If <i class="arg">-array boolean</i> is specified as true, then 2 arguments are
appended corresponding to the name of the variable and the index,
otherwise 1 argument is appended containing the name of variable.
The <i class="arg">commandPrefix</i> code is run in the same scope as the variable
is read.</p></dd>
</dl>
</div>
<div id="section3" class="doctools_section"><h2><a name="section3">EXAMPLES</a></h2>
<pre class="doctools_example">
	::lazyset::variable page {apply {{name} {
		package require http
		set token [http::geturl http://www.tcl.tk/]
		set data [http::data $token]
		return $data
	}}}
	puts $page
</pre>
<pre class="doctools_example">
	::lazyset::variable -array true page {apply {{name index} {
		package require http
		set token [http::geturl $index]
		set data [http::data $token]
		return $data
	}}}
	puts $page(http://www.tcl.tk/)
</pre>
<pre class="doctools_example">
	::lazyset::variable -appendArgs false simple {
		return -level 0 42
	}
	puts $simple
</pre>
</div>
<div id="section4" class="doctools_section"><h2><a name="section4">AUTHORS</a></h2>
<p>Roy Keene</p>
</div>
<div id="section5" class="doctools_section"><h2><a name="section5">Bugs, Ideas, Feedback</a></h2>
<p>This document, and the package it describes, will undoubtedly contain
bugs and other problems.
Please report such in the category <em>utility</em> of the
<a href="http://core.tcl.tk/tcllib/reportlist">Tcllib Trackers</a>.
Please also report any ideas for enhancements you may have for either
package and/or documentation.</p>
<p>When proposing code changes, please provide <em>unified diffs</em>,
i.e the output of <b class="const">diff -u</b>.</p>
<p>Note further that <em>attachments</em> are strongly preferred over
inlined patches. Attachments can be made by going to the <b class="const">Edit</b>
form of the ticket immediately after its creation, and then using the
left-most button in the secondary navigation bar.</p>
</div>
<div id="category" class="doctools_section"><h2><a name="category">Category</a></h2>
<p>Utility</p>
</div>
<div id="copyright" class="doctools_section"><h2><a name="copyright">Copyright</a></h2>
<p>Copyright &copy; 2018 Roy Keene</p>
</div>
</div></body></html>

<dd><p>Compares two levels (including unique abbreviations) with respect to
their priority. This command can be used by the -command option of
lsort. The result is one of -1, 0 or 1 or an error. A result of -1
signals that level1 is of less priority than level2. 0 signals that
both levels have the same priority. 1 signals that level1 has higher
priority than level2.</p></dd>
<dt><a name="8"><b class="cmd">::log::lvSuppress</b> <i class="arg">level</i> {<i class="arg">suppress</i> 1}</a></dt>

<dd><p>(Un)suppresses the output of messages having the specified
level. Unique abbreviations for the level are allowed here too.</p></dd>
<dt><a name="9"><b class="cmd">::log::lvSuppressLE</b> <i class="arg">level</i> {<i class="arg">suppress</i> 1}</a></dt>

<dd><p>(Un)suppresses the output of messages having the specified level or
one of lesser priority. Unique abbreviations for the level are allowed
here too.</p></dd>
<dt><a name="10"><b class="cmd">::log::lvIsSuppressed</b> <i class="arg">level</i></a></dt>
<dd><p>Asks the package whether the specified level is currently
suppressed. Unique abbreviations of level names are allowed.</p></dd>
<dt><a name="11"><b class="cmd">::log::lvCmd</b> <i class="arg">level</i> <i class="arg">cmd</i></a></dt>
<dd><p>Defines for the specified level with which command to write the

<li><p><em>polyline</em> - a list of an even number of coordinates,
interpreted as the x- and y-coordinates of an ordered set of points.</p></li>
<li><p><em>polygon</em> - like a polyline, but the implicit assumption is that
the polyline is closed (if the first and last points do not coincide,
the missing segment is automatically added).</p></li>
<li><p><em>point set</em> - again a list of an even number of coordinates, but
the points are regarded without any ordering.</p></li>
<li><p><em>circle</em> - a list of three numbers, the first two are the coordinates of the
centre and the third is the radius.</p></li>
</ul>
</div>
<div id="section2" class="doctools_section"><h2><a name="section2">PROCEDURES</a></h2>
<p>The package defines the following public procedures:</p>
<dl class="doctools_definitions">
<dt><a name="1"><b class="cmd">::math::geometry::+</b> <i class="arg">point1</i> <i class="arg">point2</i></a></dt>

<dd><p>Line to be checked</p></dd>
<dt>list <i class="arg">circle</i></dt>
<dd><p>Circle that may or may not be intersected</p></dd>
</dl></dd>
<dt><a name="47"><b class="cmd">::math::geometry::intersectionCircleWithCircle</b> <i class="arg">circle1</i> <i class="arg">circle2</i></a></dt>
<dd><p>Determine the points at which the given two circles intersect. There can
be zero, one or two points. (If the two circles touch the circle or are very close,
then one point is returned. An arbitrary margin of 1.0e-10 times the mean of the radii of
the two circles is used to determine this situation.)</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">circle1</i></dt>
<dd><p>First circle</p></dd>
<dt>list <i class="arg">circle2</i></dt>
<dd><p>Second circle</p></dd>
</dl></dd>
<dt><a name="48"><b class="cmd">::math::geometry::tangentLinesToCircle</b> <i class="arg">point</i> <i class="arg">circle</i></a></dt>

<!DOCTYPE html><html><head>
<title>math::numtheory - Tcl Math Library</title>
<style type="text/css"><!--
    HTML {
	background: 	#FFFFFF;
	color: 		black;
    }

| <a href="../../../toc.html">Table Of Contents</a>
| <a href="../../../../index.html">Keyword Index</a>
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 ] <hr>
<div class="doctools">
<h1 class="doctools_title">math::numtheory(n) 1.1.1 tcllib &quot;Tcl Math Library&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>math::numtheory - Number Theory</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl <span class="opt">?8.5?</span></b></li>
<li>package require <b class="pkgname">math::numtheory <span class="opt">?1.1.1?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">math::numtheory::isprime</b> <i class="arg">N</i> <span class="opt">?<i class="arg">option</i> <i class="arg">value</i> ...?</span></a></li>
<li><a href="#2"><b class="cmd">math::numtheory::firstNprimes</b> <i class="arg">N</i></a></li>
<li><a href="#3"><b class="cmd">math::numtheory::primesLowerThan</b> <i class="arg">N</i></a></li>
<li><a href="#4"><b class="cmd">math::numtheory::primeFactors</b> <i class="arg">N</i></a></li>
<li><a href="#5"><b class="cmd">math::numtheory::primesLowerThan</b> <i class="arg">N</i></a></li>
<li><a href="#6"><b class="cmd">math::numtheory::primeFactors</b> <i class="arg">N</i></a></li>
<li><a href="#7"><b class="cmd">math::numtheory::uniquePrimeFactors</b> <i class="arg">N</i></a></li>
<li><a href="#8"><b class="cmd">math::numtheory::factors</b> <i class="arg">N</i></a></li>
<li><a href="#9"><b class="cmd">math::numtheory::totient</b> <i class="arg">N</i></a></li>
<li><a href="#10"><b class="cmd">math::numtheory::moebius</b> <i class="arg">N</i></a></li>
<li><a href="#11"><b class="cmd">math::numtheory::legendre</b> <i class="arg">a</i> <i class="arg">p</i></a></li>
<li><a href="#12"><b class="cmd">math::numtheory::jacobi</b> <i class="arg">a</i> <i class="arg">b</i></a></li>
<li><a href="#13"><b class="cmd">math::numtheory::gcd</b> <i class="arg">m</i> <i class="arg">n</i></a></li>
<li><a href="#14"><b class="cmd">math::numtheory::lcm</b> <i class="arg">m</i> <i class="arg">n</i></a></li>
<li><a href="#15"><b class="cmd">math::numtheory::numberPrimesGauss</b> <i class="arg">N</i></a></li>
<li><a href="#16"><b class="cmd">math::numtheory::numberPrimesLegendre</b> <i class="arg">N</i></a></li>
<li><a href="#17"><b class="cmd">math::numtheory::numberPrimesLegendreModified</b> <i class="arg">N</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>This package is for collecting various number-theoretic operations, with
a slight bias to prime numbers.</p>
<dl class="doctools_definitions">

</dl></dd>
<dt><a name="4"><b class="cmd">math::numtheory::primeFactors</b> <i class="arg">N</i></a></dt>
<dd><p>Return a list of the prime numbers in the number N</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number to be factorised</p></dd>
</dl></dd>
<dt><a name="5"><b class="cmd">math::numtheory::primesLowerThan</b> <i class="arg">N</i></a></dt>
<dd><p>Return the prime numbers lower/equal to N</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Maximum number to consider</p></dd>
</dl></dd>
<dt><a name="6"><b class="cmd">math::numtheory::primeFactors</b> <i class="arg">N</i></a></dt>
<dd><p>Return a list of the prime numbers in the number N</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number to be factorised</p></dd>
</dl></dd>
<dt><a name="7"><b class="cmd">math::numtheory::uniquePrimeFactors</b> <i class="arg">N</i></a></dt>
<dd><p>Return a list of the <em>unique</em> prime numbers in the number N</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number to be factorised</p></dd>
</dl></dd>
<dt><a name="8"><b class="cmd">math::numtheory::factors</b> <i class="arg">N</i></a></dt>
<dd><p>Return a list of all <em>unique</em> factors in the number N, including 1 and N itself</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number to be factorised</p></dd>
</dl></dd>
<dt><a name="9"><b class="cmd">math::numtheory::totient</b> <i class="arg">N</i></a></dt>
<dd><p>Evaluate the Euler totient function for the number N (number of numbers
relatively prime to N)</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number in question</p></dd>
</dl></dd>
<dt><a name="10"><b class="cmd">math::numtheory::moebius</b> <i class="arg">N</i></a></dt>
<dd><p>Evaluate the Moebius function for the number N</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number in question</p></dd>
</dl></dd>
<dt><a name="11"><b class="cmd">math::numtheory::legendre</b> <i class="arg">a</i> <i class="arg">p</i></a></dt>
<dd><p>Evaluate the Legendre symbol (a/p)</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">a</i> (in)</dt>
<dd><p>Upper number in the symbol</p></dd>
<dt>integer <i class="arg">p</i> (in)</dt>
<dd><p>Lower number in the symbol (must be non-zero)</p></dd>
</dl></dd>
<dt><a name="12"><b class="cmd">math::numtheory::jacobi</b> <i class="arg">a</i> <i class="arg">b</i></a></dt>
<dd><p>Evaluate the Jacobi symbol (a/b)</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">a</i> (in)</dt>
<dd><p>Upper number in the symbol</p></dd>
<dt>integer <i class="arg">b</i> (in)</dt>
<dd><p>Lower number in the symbol (must be odd)</p></dd>
</dl></dd>
<dt><a name="13"><b class="cmd">math::numtheory::gcd</b> <i class="arg">m</i> <i class="arg">n</i></a></dt>
<dd><p>Return the greatest common divisor of <i class="term">m</i> and <i class="term">n</i></p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">m</i> (in)</dt>
<dd><p>First number</p></dd>
<dt>integer <i class="arg">n</i> (in)</dt>
<dd><p>Second number</p></dd>
</dl></dd>
<dt><a name="14"><b class="cmd">math::numtheory::lcm</b> <i class="arg">m</i> <i class="arg">n</i></a></dt>
<dd><p>Return the lowest common multiple of <i class="term">m</i> and <i class="term">n</i></p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">m</i> (in)</dt>
<dd><p>First number</p></dd>
<dt>integer <i class="arg">n</i> (in)</dt>
<dd><p>Second number</p></dd>
</dl></dd>
<dt><a name="15"><b class="cmd">math::numtheory::numberPrimesGauss</b> <i class="arg">N</i></a></dt>
<dd><p>Estimate the number of primes according the formula by Gauss.</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number in question</p></dd>
</dl></dd>
<dt><a name="16"><b class="cmd">math::numtheory::numberPrimesLegendre</b> <i class="arg">N</i></a></dt>
<dd><p>Estimate the number of primes according the formula by Legendre.</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number in question</p></dd>
</dl></dd>
<dt><a name="17"><b class="cmd">math::numtheory::numberPrimesLegendreModified</b> <i class="arg">N</i></a></dt>
<dd><p>Estimate the number of primes according the modified formula by Legendre.</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">N</i> (in)</dt>
<dd><p>Number in question</p></dd>
</dl></dd>
</dl>
</div>

<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.5</b></li>
<li>package require <b class="pkgname">math::statistics 1</b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::math::statistics::mean</b> <i class="arg">data</i></a></li>
<li><a href="#2"><b class="cmd">::math::statistics::min</b> <i class="arg">data</i></a></li>
<li><a href="#3"><b class="cmd">::math::statistics::max</b> <i class="arg">data</i></a></li>
<li><a href="#4"><b class="cmd">::math::statistics::number</b> <i class="arg">data</i></a></li>

<li><a href="#37"><b class="cmd">::math::statistics::analyse-Kruskal-Wallis</b> <i class="arg">args</i></a></li>
<li><a href="#38"><b class="cmd">::math::statistics::group-rank</b> <i class="arg">args</i></a></li>
<li><a href="#39"><b class="cmd">::math::statistics::test-Wilcoxon</b> <i class="arg">sample_a</i> <i class="arg">sample_b</i></a></li>
<li><a href="#40"><b class="cmd">::math::statistics::spearman-rank</b> <i class="arg">sample_a</i> <i class="arg">sample_b</i></a></li>
<li><a href="#41"><b class="cmd">::math::statistics::spearman-rank-extended</b> <i class="arg">sample_a</i> <i class="arg">sample_b</i></a></li>
<li><a href="#42"><b class="cmd">::math::statistics::kernel-density</b> <i class="arg">data</i> opt <i class="arg">-option value</i> ...</a></li>
<li><a href="#43"><b class="cmd">::math::statistics::bootstrap</b> <i class="arg">data</i> <i class="arg">sampleSize</i> <span class="opt">?numberSamples?</span></a></li>
<li><a href="#44"><b class="cmd">::math::statistics::wasserstein-distance</b> <i class="arg">prob1</i> <i class="arg">prob2</i></a></li>
<li><a href="#45"><b class="cmd">::math::statistics::kl-divergence</b> <i class="arg">prob1</i> <i class="arg">prob2</i></a></li>
<li><a href="#46"><b class="cmd">::math::statistics::logistic-model</b> <i class="arg">xdata</i> <i class="arg">ydata</i></a></li>
<li><a href="#47"><b class="cmd">::math::statistics::logistic-probability</b> <i class="arg">coeffs</i> <i class="arg">x</i></a></li>
<li><a href="#48"><b class="cmd">::math::statistics::tstat</b> <i class="arg">dof</i> <span class="opt">?alpha?</span></a></li>
<li><a href="#49"><b class="cmd">::math::statistics::mv-wls</b> <i class="arg">wt1</i> <i class="arg">weights_and_values</i></a></li>
<li><a href="#50"><b class="cmd">::math::statistics::mv-ols</b> <i class="arg">values</i></a></li>
<li><a href="#51"><b class="cmd">::math::statistics::pdf-normal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></li>
<li><a href="#52"><b class="cmd">::math::statistics::pdf-lognormal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></li>
<li><a href="#53"><b class="cmd">::math::statistics::pdf-exponential</b> <i class="arg">mean</i> <i class="arg">value</i></a></li>
<li><a href="#54"><b class="cmd">::math::statistics::pdf-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">value</i></a></li>
<li><a href="#55"><b class="cmd">::math::statistics::pdf-gamma</b> <i class="arg">alpha</i> <i class="arg">beta</i> <i class="arg">value</i></a></li>
<li><a href="#56"><b class="cmd">::math::statistics::pdf-poisson</b> <i class="arg">mu</i> <i class="arg">k</i></a></li>
<li><a href="#57"><b class="cmd">::math::statistics::pdf-chisquare</b> <i class="arg">df</i> <i class="arg">value</i></a></li>
<li><a href="#58"><b class="cmd">::math::statistics::pdf-student-t</b> <i class="arg">df</i> <i class="arg">value</i></a></li>
<li><a href="#59"><b class="cmd">::math::statistics::pdf-gamma</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">value</i></a></li>
<li><a href="#60"><b class="cmd">::math::statistics::pdf-beta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">value</i></a></li>
<li><a href="#61"><b class="cmd">::math::statistics::pdf-weibull</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></li>
<li><a href="#62"><b class="cmd">::math::statistics::pdf-gumbel</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></li>
<li><a href="#63"><b class="cmd">::math::statistics::pdf-pareto</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></li>
<li><a href="#64"><b class="cmd">::math::statistics::pdf-cauchy</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></li>
<li><a href="#65"><b class="cmd">::math::statistics::cdf-normal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></li>
<li><a href="#66"><b class="cmd">::math::statistics::cdf-lognormal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></li>
<li><a href="#67"><b class="cmd">::math::statistics::cdf-exponential</b> <i class="arg">mean</i> <i class="arg">value</i></a></li>
<li><a href="#68"><b class="cmd">::math::statistics::cdf-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">value</i></a></li>
<li><a href="#69"><b class="cmd">::math::statistics::cdf-students-t</b> <i class="arg">degrees</i> <i class="arg">value</i></a></li>
<li><a href="#70"><b class="cmd">::math::statistics::cdf-gamma</b> <i class="arg">alpha</i> <i class="arg">beta</i> <i class="arg">value</i></a></li>
<li><a href="#71"><b class="cmd">::math::statistics::cdf-poisson</b> <i class="arg">mu</i> <i class="arg">k</i></a></li>
<li><a href="#72"><b class="cmd">::math::statistics::cdf-beta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">value</i></a></li>
<li><a href="#73"><b class="cmd">::math::statistics::cdf-weibull</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></li>
<li><a href="#74"><b class="cmd">::math::statistics::cdf-gumbel</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></li>
<li><a href="#75"><b class="cmd">::math::statistics::cdf-pareto</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></li>
<li><a href="#76"><b class="cmd">::math::statistics::cdf-cauchy</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></li>
<li><a href="#77"><b class="cmd">::math::statistics::cdf-F</b> <i class="arg">nf1</i> <i class="arg">nf2</i> <i class="arg">value</i></a></li>
<li><a href="#78"><b class="cmd">::math::statistics::empirical-distribution</b> <i class="arg">values</i></a></li>
<li><a href="#79"><b class="cmd">::math::statistics::random-normal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">number</i></a></li>
<li><a href="#80"><b class="cmd">::math::statistics::random-lognormal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">number</i></a></li>
<li><a href="#81"><b class="cmd">::math::statistics::random-exponential</b> <i class="arg">mean</i> <i class="arg">number</i></a></li>
<li><a href="#82"><b class="cmd">::math::statistics::random-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">number</i></a></li>
<li><a href="#83"><b class="cmd">::math::statistics::random-gamma</b> <i class="arg">alpha</i> <i class="arg">beta</i> <i class="arg">number</i></a></li>
<li><a href="#84"><b class="cmd">::math::statistics::random-poisson</b> <i class="arg">mu</i> <i class="arg">number</i></a></li>
<li><a href="#85"><b class="cmd">::math::statistics::random-chisquare</b> <i class="arg">df</i> <i class="arg">number</i></a></li>
<li><a href="#86"><b class="cmd">::math::statistics::random-student-t</b> <i class="arg">df</i> <i class="arg">number</i></a></li>
<li><a href="#87"><b class="cmd">::math::statistics::random-beta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">number</i></a></li>
<li><a href="#88"><b class="cmd">::math::statistics::random-weibull</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">number</i></a></li>
<li><a href="#89"><b class="cmd">::math::statistics::random-gumbel</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">number</i></a></li>
<li><a href="#90"><b class="cmd">::math::statistics::random-pareto</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">number</i></a></li>
<li><a href="#91"><b class="cmd">::math::statistics::random-cauchy</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">number</i></a></li>
<li><a href="#92"><b class="cmd">::math::statistics::histogram-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">limits</i> <i class="arg">number</i></a></li>
<li><a href="#93"><b class="cmd">::math::statistics::incompleteGamma</b> <i class="arg">x</i> <i class="arg">p</i> <span class="opt">?tol?</span></a></li>
<li><a href="#94"><b class="cmd">::math::statistics::incompleteBeta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">x</i> <span class="opt">?tol?</span></a></li>
<li><a href="#95"><b class="cmd">::math::statistics::estimate-pareto</b> <i class="arg">values</i></a></li>
<li><a href="#96"><b class="cmd">::math::statistics::filter</b> <i class="arg">varname</i> <i class="arg">data</i> <i class="arg">expression</i></a></li>
<li><a href="#97"><b class="cmd">::math::statistics::map</b> <i class="arg">varname</i> <i class="arg">data</i> <i class="arg">expression</i></a></li>
<li><a href="#98"><b class="cmd">::math::statistics::samplescount</b> <i class="arg">varname</i> <i class="arg">list</i> <i class="arg">expression</i></a></li>
<li><a href="#99"><b class="cmd">::math::statistics::subdivide</b></a></li>
<li><a href="#100"><b class="cmd">::math::statistics::plot-scale</b> <i class="arg">canvas</i> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">ymin</i> <i class="arg">ymax</i></a></li>
<li><a href="#101"><b class="cmd">::math::statistics::plot-xydata</b> <i class="arg">canvas</i> <i class="arg">xdata</i> <i class="arg">ydata</i> <i class="arg">tag</i></a></li>
<li><a href="#102"><b class="cmd">::math::statistics::plot-xyline</b> <i class="arg">canvas</i> <i class="arg">xdata</i> <i class="arg">ydata</i> <i class="arg">tag</i></a></li>
<li><a href="#103"><b class="cmd">::math::statistics::plot-tdata</b> <i class="arg">canvas</i> <i class="arg">tdata</i> <i class="arg">tag</i></a></li>
<li><a href="#104"><b class="cmd">::math::statistics::plot-tline</b> <i class="arg">canvas</i> <i class="arg">tdata</i> <i class="arg">tag</i></a></li>
<li><a href="#105"><b class="cmd">::math::statistics::plot-histogram</b> <i class="arg">canvas</i> <i class="arg">counts</i> <i class="arg">limits</i> <i class="arg">tag</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>The <b class="package">math::statistics</b> package contains functions and procedures for
basic statistical data analysis, such as:</p>
<ul class="doctools_itemized">

<dt>list <i class="arg">data</i></dt>
<dd><p>List of values to chose from</p></dd>
<dt>int <i class="arg">sampleSize</i></dt>
<dd><p>Number of values per sample</p></dd>
<dt>int <i class="arg">numberSamples</i></dt>
<dd><p>Number of samples (default: 1)</p></dd>
</dl></dd>
<dt><a name="44"><b class="cmd">::math::statistics::wasserstein-distance</b> <i class="arg">prob1</i> <i class="arg">prob2</i></a></dt>
<dd><p>Compute the Wasserstein distance or earth mover's distance for two equidstantly spaced histograms
or probability densities. The histograms need not to be normalised to sum to one,
but they must have the same number of entries.</p>
<p>Note: the histograms are assumed to be based on the same equidistant intervals.
As the bounds are not passed, the value is expressed in the length of the intervals.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">prob1</i></dt>
<dd><p>List of values for the first histogram/probability density</p></dd>
<dt>list <i class="arg">prob2</i></dt>
<dd><p>List of values for the second histogram/probability density</p></dd>
</dl></dd>
<dt><a name="45"><b class="cmd">::math::statistics::kl-divergence</b> <i class="arg">prob1</i> <i class="arg">prob2</i></a></dt>
<dd><p>Compute the Kullback-Leibler (KL) divergence for two equidstantly spaced histograms
or probability densities. The histograms need not to be normalised to sum to one,
but they must have the same number of entries.</p>
<p>Note: the histograms are assumed to be based on the same equidistant intervals.
As the bounds are not passed, the value is expressed in the length of the intervals.</p>
<p>Note also that the KL divergence is not symmetric and that the second histogram
should not contain zeroes in places where the first histogram has non-zero values.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">prob1</i></dt>
<dd><p>List of values for the first histogram/probability density</p></dd>
<dt>list <i class="arg">prob2</i></dt>
<dd><p>List of values for the second histogram/probability density</p></dd>
</dl></dd>
<dt><a name="46"><b class="cmd">::math::statistics::logistic-model</b> <i class="arg">xdata</i> <i class="arg">ydata</i></a></dt>
<dd><p>Estimate the coefficients of the logistic model that fits the data best. The data consist
of independent x-values and the outcome 0 or 1 for each of the x-values. The result
can be used to estimate the probability that a certain x-value gives 1.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">xdata</i></dt>
<dd><p>List of values for which the success (1) or failure (0) is known</p></dd>
<dt>list <i class="arg">ydata</i></dt>
<dd><p>List of successes or failures corresponding to each value in <i class="term">xdata</i>.</p></dd>
</dl></dd>
<dt><a name="47"><b class="cmd">::math::statistics::logistic-probability</b> <i class="arg">coeffs</i> <i class="arg">x</i></a></dt>
<dd><p>Calculate the probability of success for the value <i class="term">x</i> given the coefficients of the
logistic model.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">coeffs</i></dt>
<dd><p>List of coefficients as determine by the <b class="cmd">logistic-model</b> command</p></dd>
<dt>float <i class="arg">x</i></dt>
<dd><p>X-value for which the probability needs to be determined</p></dd>
</dl></dd>
</dl>
</div>
<div id="section3" class="doctools_section"><h2><a name="section3">MULTIVARIATE LINEAR REGRESSION</a></h2>
<p>Besides the linear regression with a single independent variable, the
statistics package provides two procedures for doing ordinary
least squares (OLS) and weighted least squares (WLS) linear regression
with several variables. They were written by Eric Kemp-Benedict.</p>
<p>In addition to these two, it provides a procedure (tstat)
for calculating the value of the t-statistic for the specified number of
degrees of freedom that is required to demonstrate a given level of
significance.</p>
<p>Note: These procedures depend on the math::linearalgebra package.</p>
<p><em>Description of the procedures</em></p>
<dl class="doctools_definitions">
<dt><a name="48"><b class="cmd">::math::statistics::tstat</b> <i class="arg">dof</i> <span class="opt">?alpha?</span></a></dt>
<dd><p>Returns the value of the t-distribution t* satisfying</p>
<pre class="doctools_example">
    P(t*)  =  1 - alpha/2
    P(-t*) =  alpha/2
</pre>
<p>for the number of degrees of freedom dof.</p>
<p>Given a sample of normally-distributed data x, with an

the given confidence level.</p>
<dl class="doctools_arguments">
<dt>int <i class="arg">dof</i></dt>
<dd><p>Number of degrees of freedom</p></dd>
<dt>float <i class="arg">alpha</i></dt>
<dd><p>Confidence level of the t-distribution. Defaults to 0.05.</p></dd>
</dl></dd>
<dt><a name="49"><b class="cmd">::math::statistics::mv-wls</b> <i class="arg">wt1</i> <i class="arg">weights_and_values</i></a></dt>
<dd><p>Carries out a weighted least squares linear regression for
the data points provided, with weights assigned to each point.</p>
<p>The linear model is of the form</p>
<pre class="doctools_example">
    y = b0 + b1 * x1 + b2 * x2 ... + bN * xN + error
</pre>
<p>and each point satisfies</p>

<dt>list <i class="arg">weights_and_values</i></dt>
<dd><p>A list consisting of: the weight for the first observation, the data
for the first observation (as a sublist), the weight for the second
observation (as a sublist) and so on. The sublists of data are organised
as lists of the value of the dependent variable y and the independent
variables x1, x2 to xN.</p></dd>
</dl></dd>
<dt><a name="50"><b class="cmd">::math::statistics::mv-ols</b> <i class="arg">values</i></a></dt>
<dd><p>Carries out an ordinary least squares linear regression for
the data points provided.</p>
<p>This procedure simply calls ::mvlinreg::wls with the weights
set to 1.0, and returns the same information.</p></dd>
</dl>
<p><em>Example of the use:</em></p>
<pre class="doctools_example">